Question 1

Find the exact value. Do not use a calculator.
- tan⁡60∘	an 60 ^ { \circ }tan60∘

Accepted Answer

A)    3\sqrt { 3 }3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)   2
C)    32\frac { \sqrt { 3 } } { 2 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    33\frac { \sqrt { 3 } } { 3 }33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) A) and D)
F) B) and D)

Question 2

Name the quadrant in which the angle θ lies. - 0">cot⁡θ<0,cos⁡θ>0\cot heta < 0 , \quad \cos heta > 0cotθ<0,cosθ>0

Accepted Answer

A)   I
B)   II
C)   III
D)   IV E) All of the above
F) None of the above

Question 3

Find an equation for the graph.
-

Accepted Answer

A)    y=5cos⁡(3x) y = 5 \cos ( 3 x ) y=5cos(3x)  
B)    y=3cos⁡(15x) y = 3 \cos \left( \frac { 1 } { 5 } x \right) y=3cos(51​x)  
C)    y=5cos⁡(13x) y = 5 \cos \left( \frac { 1 } { 3 } x \right) y=5cos(31​x)  
D)    y=3cos⁡(5x) y = 3 \cos ( 5 x ) y=3cos(5x) E) A) and C)
F) B) and C)

Question 4

Find the exact value. Do not use a calculator.
- cos⁡π\cos \picosπ

Accepted Answer

A)   1
B)    −1- 1−1 
C)   0
D)   undefined E) B) and C)
F) All of the above

Question 5

Graph the function.
- y=csc⁡(14x) y = \csc \left( \frac { 1 } { 4 } x \right) y=csc(41​x)

Accepted Answer

A)  
B)  
C)  
D)   E) C) and D)
F) B) and C)

Question 6

Convert the angle to D° M' S'' form. Round the answer to the nearest second.
- 112.56∘112.56 ^ { \circ }112.56∘

Accepted Answer

A)    112∘34′36′′112 ^ { \circ } 34 ^ { \prime } 36 ^ { \prime \prime }112∘34′36′′ 
B)    112∘33′56′′112 ^ { \circ } 33 ^ { \prime } 56 ^ { \prime \prime }112∘33′56′′ 
C)    112∘33′36′′112 ^ { \circ } 33 ^ { \prime } 36 ^ { \prime \prime }112∘33′36′′ 
D)    112∘31′56′′112 ^ { \circ } 31 ^ { \prime } 56 ^ { \prime \prime }112∘31′56′′E) B) and C)
F) A) and D)

Question 7

Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
- csc⁡(−30∘) \csc \left( - 30 ^ { \circ } \right) csc(−30∘)

Accepted Answer

A)   2
B)    −233- \frac { 2 \sqrt { 3 } } { 3 }−323c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    −2- 2−2 
D)    233\frac { 2 \sqrt { 3 } } { 3 }323c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) None of the above
F) A) and C)

Question 8

Find the exact value of the expression. Do not use a calculator.
- cos⁡60∘+tan⁡60∘\cos 60 ^ { \circ } + 	an 60 ^ { \circ }cos60∘+tan60∘

Accepted Answer

A)    232 \sqrt { 3 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    1+32\frac { 1 + \sqrt { 3 } } { 2 }21+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    332\frac { 3 \sqrt { 3 } } { 2 }233c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    1+232\frac { 1 + 2 \sqrt { 3 } } { 2 }21+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) None of the above
F) B) and D)

Question 9

Solve the problem.
-If  tan⁡θ=−0.4	an 	heta = - 0.4tanθ=−0.4 , find the value of  tan⁡θ+tan⁡(θ+π) +tan⁡(θ+2π) 	an 	heta + 	an ( 	heta + \pi )  + 	an ( 	heta + 2 \pi ) tanθ+tan(θ+π) +tan(θ+2π)  .

Accepted Answer

A)    −1.2- 1.2−1.2 
B)    0.80.80.8 
C)    −1.2+3π- 1.2 + 3 \pi−1.2+3π 
D)   undefined E) A) and D)
F) B) and D)

Question 10

Solve the problem.
-The blade of a windshield wiper sweeps out an angle of  135∘135 ^ { \circ }135∘  in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest  0.10.10.1  square inch.)

Accepted Answer

A)    1041.81041.81041.8  in  2^ { 2 }2 
B)    1105.3in21105.3 \mathrm { in } ^ { 2 }1105.3in2 
C)    948.3948.3948.3  in  2^ { 2 }2 
D)    1036.7in21036.7 \mathrm { in } ^ { 2 }1036.7in2E) All of the above
F) A) and D)

Question 11

In the problem, t is a real number and P = (x, y)  is the point on the unit circle that corresponds to t. Find the exact value of
the indicated trigonometric function of t.
- (−398,58) \left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right)  \quad(−839​​,85​)   Find  cos⁡t\cos tcost

Accepted Answer

A)   −395 - \frac { \sqrt { 39 } } { 5 }−539c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    58\frac { 5 } { 8 }85​ 
C)   −83939 - \frac { 8 \sqrt { 39 } } { 39 }−39839c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    −398- \frac { \sqrt { 39 } } { 8 }−839c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) None of the above
F) A) and D)

Question 12

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator.
- tan⁡40∘cot⁡40∘	an 40 ^ { \circ } \cot 40 ^ { \circ }tan40∘cot40∘

Accepted Answer

A)    −1- 1−1 
B)   40
C)   1
D)   0 E) All of the above
F) A) and B)

Question 13

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
- r=9r = 9r=9  feet,  A=39A = 39A=39  square feet,  θ=	heta =θ=  ?

Accepted Answer

A)    0.480.480.48  radians
B)   3,159 radians
C)    0.960.960.96  radians
D)    1,579.51,579.51,579.5  radians E) All of the above
F) A) and B)

Question 14

Find the exact value of the expression. Do not use a calculator.
- tan⁡150∘cos⁡210∘	an 150 ^ { \circ } \cos 210 ^ { \circ }tan150∘cos210∘

Accepted Answer

A)    23+36\frac { 2 \sqrt { 3 } + 3 } { 6 }623c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+3​ 
B)    33+236\frac { 3 \sqrt { 3 } + 2 \sqrt { 3 } } { 6 }633c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    3+12\frac { \sqrt { 3 } + 1 } { 2 }23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+1​ 
D)    −536- \frac { 5 \sqrt { 3 } } { 6 }−653c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) All of the above
F) B) and C)

Question 15

Draw the angle.
- 2π3\frac { 2 \pi } { 3 }32π​

Accepted Answer

A)  
B)  
C)  
D)   E) B) and D)
F) B) and C)

Question 16

Use transformations to graph the function.
- y=cos⁡x−1y=\cos x-1y=cosx−1

Accepted Answer

A)  
B)  
C)  
D)   E) All of the above
F) None of the above

Question 17

Use transformations to graph the function.
- y=4cos⁡xy=4 \cos xy=4cosx

Accepted Answer

A)  
B)  
C)   
D)   E) A) and B)
F) A) and D)

Question 18

Find the length s. Round the answer to three decimal places.
-

Accepted Answer

A)    3.84 m3.84 \mathrm {~m}3.84 m 
B)    2.793 m2.793 \mathrm {~m}2.793 m 
C)    3.491 m3.491 \mathrm {~m}3.491 m 
D)    3.142 m3.142 \mathrm {~m}3.142 mE) None of the above
F) A) and B)

Question 19

Use transformations to graph the function.
- y=5cos⁡(π−x) y=5 \cos (\pi-x) y=5cos(π−x)

Accepted Answer

A)  
B)  
C)  
D)   E) B) and D)
F) A) and D)

Question 20

In the problem, t is a real number and P = (x, y)  is the point on the unit circle that corresponds to t. Find the exact value of
the indicated trigonometric function of t.
- (29,779) \left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right)  \quad(92​,977​​)   Find  sin⁡t\sin tsint

Accepted Answer

A)    772\frac { \sqrt { 77 } } { 2 }277c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    779\frac { \sqrt { 77 } } { 9 }977c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    27777\frac { 2 \sqrt { 77 } } { 77 }77277c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    29\frac { 2 } { 9 }92​E) A) and B)
F) C) and D)

Exam 5: Trigonometric Functions

Find the exact value of the expression. Do not use a calculator. - tan⁡150∘cos⁡210∘\tan 150 ^ { \circ } \cos 210 ^ { \circ }tan150∘cos210∘

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Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - tan⁡40∘cot⁡40∘\tan 40 ^ { \circ } \cot 40 ^ { \circ }tan40∘cot40∘

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Use transformations to graph the function. - y=5cos⁡(π−x) y=5 \cos (\pi-x) y=5cos(π−x)

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Convert the angle to D° M' S'' form. Round the answer to the nearest second. - 112.56∘112.56 ^ { \circ }112.56∘

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Graph the function. - y=csc⁡(14x) y = \csc \left( \frac { 1 } { 4 } x \right) y=csc(41​x)

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Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - csc⁡(−30∘) \csc \left( - 30 ^ { \circ } \right) csc(−30∘)

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Solve the problem. -If tan⁡θ=−0.4\tan \theta = - 0.4tanθ=−0.4 , find the value of tan⁡θ+tan⁡(θ+π) +tan⁡(θ+2π) \tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi ) tanθ+tan(θ+π) +tan(θ+2π) .

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Find the exact value. Do not use a calculator. - tan⁡60∘\tan 60 ^ { \circ }tan60∘

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Find an equation for the graph. -

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If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - r=9r = 9r=9 feet, A=39A = 39A=39 square feet, θ=\theta =θ= ?

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Use transformations to graph the function. - y=4cos⁡xy=4 \cos xy=4cosx

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Name the quadrant in which the angle θ lies. - cot⁡θ<0,cos⁡θ>0\cot \theta < 0 , \quad \cos \theta > 0cotθ<0,cosθ>0

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Draw the angle. - 2π3\frac { 2 \pi } { 3 }32π​

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Find the length s. Round the answer to three decimal places. -

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Find the exact value. Do not use a calculator. - cos⁡π\cos \picosπ

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Use transformations to graph the function. - y=cos⁡x−1y=\cos x-1y=cosx−1

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In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - (29,779) \left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad(92​,977​​) Find sin⁡t\sin tsint

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Find the exact value of the expression. Do not use a calculator. - cos⁡60∘+tan⁡60∘\cos 60 ^ { \circ } + \tan 60 ^ { \circ }cos60∘+tan60∘

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Find the exact value of the expression. Do not use a calculator. - $\tan 150 ^ { \circ } \cos 210 ^ { \circ }$

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Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

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Use transformations to graph the function. - $y=5 \cos (\pi-x)$ $Use transformations to graph the function. - y=5 \cos (\pi-x) A) B) C) D)$

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Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $112.56 ^ { \circ }$

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Graph the function. - $y = \csc \left( \frac { 1 } { 4 } x \right)$ $Graph the function. - y = \csc \left( \frac { 1 } { 4 } x \right) A) B) C) D)$

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Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - 30 ^ { \circ } \right)$

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Solve the problem. -If $\tan \theta = - 0.4$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

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Find the exact value. Do not use a calculator. - $\tan 60 ^ { \circ }$

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Find an equation for the graph. - $Find an equation for the graph. - A) y = 5 \cos ( 3 x ) B) y = 3 \cos \left( \frac { 1 } { 5 } x \right) C) y = 5 \cos \left( \frac { 1 } { 3 } x \right) D) y = 3 \cos ( 5 x )$

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If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $r = 9$ feet, $A = 39$ square feet, $\theta =$ ?

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Use transformations to graph the function. - $y=4 \cos x$ $Use transformations to graph the function. - y=4 \cos x A) B) C) D)$

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Name the quadrant in which the angle θ lies. - $\cot \theta < 0 , \quad \cos \theta > 0$

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Draw the angle. - $\frac { 2 \pi } { 3 }$

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Find the length s. Round the answer to three decimal places. - $Find the length s. Round the answer to three decimal places. - A) 3.84 \mathrm {~m} B) 2.793 \mathrm {~m} C) 3.491 \mathrm {~m} D) 3.142 \mathrm {~m}$

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Find the exact value. Do not use a calculator. - $\cos \pi$

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Use transformations to graph the function. - $y=\cos x-1$ $Use transformations to graph the function. - y=\cos x-1 A) B) C) D)$

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In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin t$

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Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

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