Question 1

Solve the problem.
-A sensor light installed on the edge of a home can detect motion for a distance of  50ft50 \mathrm { ft }50ft . in front and with a range of motion of  238∘238 ^ { \circ }238∘ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

Accepted Answer

A)    5192.35ft25192.35 \mathrm { ft } ^ { 2 }5192.35ft2 
B)    10,384.81ft210,384.81 \mathrm { ft } ^ { 2 }10,384.81ft2 
C)    10,384.71ft210,384.71 \mathrm { ft } ^ { 2 }10,384.71ft2 
D)    5192.25ft25192.25 \mathrm { ft } ^ { 2 }5192.25ft2E) A) and C)
F) None of the above

Question 2

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
- sin⁡s=0.8454\sin \mathrm { s } = 0.8454sins=0.8454

Accepted Answer

A)    −0.8657- 0.8657−0.8657 
B)    0.27590.27590.2759 
C)    1.00731.00731.0073 
D)    2.13432.13432.1343E) A) and C)
F) A) and D)

Question 3

Find the exact circular function value.
- cot⁡−11π6\cot \frac { - 11 \pi } { 6 }cot6−11π​

Accepted Answer

A)    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'/>​​ 
B)    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'/>​ 
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)    −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'/>​E) A) and B)
F) A) and C)

Question 4

Solve the problem.
-The minute hand of a clock is 14 inches long. What distance does its tip move in 23 minutes? Give an exact answer.

Accepted Answer

A)    16130πin\frac { 161 } { 30 } \pi \mathrm { in }30161​πin .
B)    23840πin\frac { 23 } { 840 } \pi \mathrm { in }84023​πin .
C)    23420πin\frac { 23 } { 420 } \pi \mathrm { in }42023​πin .
D)    16115πin\frac { 161 } { 15 } \pi \mathrm { in }15161​πin . E) A) and B)
F) None of the above

Question 5

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
-Find  cos⁡θ\cos 	hetacosθ

Accepted Answer

A)    725\frac { 7 } { 25 }257​ 
B)    724\frac { 7 } { 24 }247​ 
C)    −725- \frac { 7 } { 25 }−257​ 
D)    −2425- \frac { 24 } { 25 }−2524​E) A) and B)
F) A) and C)

Question 6

Find the exact circular function value.
- tan⁡7π6	an \frac { 7 \pi } { 6 }tan67π​

Accepted Answer

A)    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'/>​​ 
B)    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'/>​​ 
C)    −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'/>​ 
D)    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'/>​E) A) and C)
F) None of the above

Question 7

Solve the problem. -The minimum length LLL of a highway sag curve can be computed by L=(θ2−θ1) S2200( h+Stan⁡α) ′\mathrm { L } = \frac { \left( heta _ { 2 } - heta _ { 1 } ight) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } an \alpha ) ^ { \prime } }L=200( h+Stanα) ′(θ2−θ1) S2 where θ1 heta _ { 1 }θ1 is the downhill grade in degrees (θ1<0∘) ,θ2\left( heta _ { 1 } < 0 ^ { \circ } ight) , heta _ { 2 }(θ1<0∘) ,θ2 is the uphill grade in degrees 0 ^ { \circ } ight) , \mathrm { S }">(θ2>0∘) ,S\left( heta _ { 2 } > 0 ^ { \circ } ight) , \mathrm { S }(θ2>0∘) ,S is the safe stopping distance for a given speed limit, hhh is the height of the headlights, and α\alphaα is the alignment of the headlights in degrees. Compute LLL for a 55 -mph speed limit, where h=1.6fth = 1.6 \mathrm { ft }h=1.6ft , α=0.8∘,θ1=−5∘,θ2=1∘\alpha = 0.8 ^ { \circ } , heta _ { 1 } = - 5 ^ { \circ } , heta _ { 2 } = 1 ^ { \circ }α=0.8∘,θ1=−5∘,θ2=1∘ , and S=336ftS = 336 \mathrm { ft }S=336ft . Round your answer to the nearest foot.

Accepted Answer

A)    525ft525 \mathrm { ft }525ft 
B)    553ft553 \mathrm { ft }553ft 
C)    568ft568 \mathrm { ft }568ft 
D)    538ft538 \mathrm { ft }538ftE) A) and B)
F) None of the above

Question 8

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
-Find  sin⁡θ\sin 	hetasinθ .

Accepted Answer

A)    −724- \frac { 7 } { 24 }−247​ 
B)    725\frac { 7 } { 25 }257​ 
C)    2425\frac { 24 } { 25 }2524​ 
D)    −2425- \frac { 24 } { 25 }−2524​E) B) and C)
F) A) and B)

Question 9

Solve the problem.
-Ignoring friction, the time,  ttt  (in seconds) , required for a block to slide down an inclined plane is given by the formula  t=2bgsin⁡θcos⁡θt = \sqrt { \frac { 2 b } { g \sin 	heta \cos 	heta } }t=gsinθcosθ2b​​  where  bbb  is the length of the base in feet and  g=32.2g = 32.2g=32.2  feet per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with a base of 12 feet at an angle of  44∘44 ^ { \circ }44∘  ? Round your answer to three decimal places.

Accepted Answer

A)    6.93sec6.93 \mathrm { sec }6.93sec 
B)    0.353sec0.353 \mathrm { sec }0.353sec 
C)    0.864sec0.864 \mathrm { sec }0.864sec 
D)    1.221sec1.221 \mathrm { sec }1.221secE) B) and D)
F) C) and D)

Question 10

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.
- 0. Determine the equation of the graph. -  A)   y = 2 \cos ( 3 x )   B)   y = - 2 \cos ( 3 x )   C)   y = - 2 \cos \left( \frac { 1 } { 3 } x \right)   D)   y = - 2 \sin ( 3 x ) " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)    y=2cos⁡(3x) y = 2 \cos ( 3 x ) y=2cos(3x)  
B)    y=−2cos⁡(3x) y = - 2 \cos ( 3 x ) y=−2cos(3x)  
C)    y=−2cos⁡(13x) y = - 2 \cos \left( \frac { 1 } { 3 } x \right) y=−2cos(31​x)  
D)    y=−2sin⁡(3x) y = - 2 \sin ( 3 x ) y=−2sin(3x) E) C) and D)
F) All of the above

Question 11

Use a table or a calculator to evaluate the function. Round to four decimal places.
- sin⁡0.2721\sin 0.2721sin0.2721

Accepted Answer

A)    0.96320.96320.9632 
B)    1.03821.03821.0382 
C)    0.26880.26880.2688 
D)    0.27900.27900.2790E) B) and D)
F) C) and D)

Question 12

Solve the problem.
-An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of  13\frac { 1 } { 3 }31​  radian has been covered, what is the linear speed of the object?

Accepted Answer

A)    3827 cm\frac { 38 } { 27 } \mathrm {~cm}2738​ cm  per sec
B)    1927 cm\frac { 19 } { 27 } \mathrm {~cm}2719​ cm  per sec
C)    19 cm19 \mathrm {~cm}19 cm  per sec
D)    57 cm57 \mathrm {~cm}57 cm  per sec E) All of the above
F) A) and B)

Question 13

Solve the problem.
-A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched  2ft2 \mathrm { ft }2ft  and released. What is the equation for the resulting oscillatory motion?

Accepted Answer

A)    s(t) =2sin⁡6ts ( t )  = 2 \sin \sqrt { 6 } ts(t) =2sin6c-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'/>​t 
B)    s(t) =12sin⁡112ts ( t )  = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 12 } } ts(t) =21​sin121​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z'/>​t 
C)    s(t) =2sin⁡16ts ( t )  = 2 \sin \sqrt { \frac { 1 } { 6 } } ts(t) =2sin61​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z'/>​t 
D)    s(t) =6sin⁡2ts ( t )  = 6 \sin \sqrt { 2 } ts(t) =6sin2c-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'/>​tE) C) and D)
F) None of the above

Question 14

Find the phase shift of the function.
- y=cos⁡(x−π2) y = \cos \left( x - \frac { \pi } { 2 } \right) y=cos(x−2π​)

Accepted Answer

A)    π2\frac { \pi } { 2 }2π​  units up
B)    π2\frac { \pi } { 2 }2π​  units to the right
C)    π2\frac { \pi } { 2 }2π​  units to the left
D)    π2\frac { \pi } { 2 }2π​  units down E) None of the above
F) A) and B)

Question 15

Solve the problem.
-Let angle  POQP O QPOQ  be designated  θ	hetaθ . Angles  PQRP Q RPQR  and  VRQV R QVRQ  are right angles. If  θ=45∘	heta = 45 ^ { \circ }θ=45∘ , find the exact length of US.

Accepted Answer

A)    22\frac { \sqrt { 2 } } { 2 }22c-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)   0
C)   1
D)    2\sqrt { 2 }2c-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) C) and D)

Question 16

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
-Find  csc⁡θ\csc 	hetacscθ .

Accepted Answer

A)    2524\frac { 25 } { 24 }2425​ 
B)    −2524- \frac { 25 } { 24 }−2425​ 
C)    −257- \frac { 25 } { 7 }−725​ 
D)    247\frac { 24 } { 7 }724​E) C) and D)
F) A) and B)

Question 17

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
- −262∘58′- 262 ^ { \circ } 58 ^ { \prime }−262∘58′

Accepted Answer

A)    −4.5696- 4.5696−4.5696 
B)    −4.5596- 4.5596−4.5596 
C)    −4.5796- 4.5796−4.5796 
D)    −4.5896- 4.5896−4.5896E) A) and C)
F) C) and D)

Question 18

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
- 86.9152∘86.9152 ^ { \circ }86.9152∘

Accepted Answer

A)    1.71701.71701.7170 
B)    1.51701.51701.5170 
C)    1.61701.61701.6170 
D)    1.81701.81701.8170E) A) and C)
F) B) and C)

Question 19

Determine the equation of the graph.
-

Accepted Answer

A)    y=−sec⁡2xy = - \sec 2 xy=−sec2x 
B)    y=sec⁡(12x) y = \sec \left( \frac { 1 } { 2 } x \right) y=sec(21​x)  
C)    y=sec⁡2xy = \sec 2 xy=sec2x 
D)    y=−sec⁡(12x) y = - \sec \left( \frac { 1 } { 2 } x \right) y=−sec(21​x) E) A) and C)
F) None of the above

Question 20

Solve the problem.
-The voltage  E\mathrm { E }E  in an electrical circuit is given by  E=3.1cos⁡140πt\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }E=3.1cos140πt , where  ttt  is time measured in seconds. Find the amplitude.

Accepted Answer

A)    3.13.13.1 
B)   140
C)    6.26.26.2 
D)    140π140 \pi140πE) B) and C)
F) A) and B)

Exam 6: The Circular Functions and Their Graphs

Find the exact circular function value. - $\cot \frac { - 11 \pi } { 6 }$

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Find the phase shift of the function. - $y = \cos \left( x - \frac { \pi } { 2 } \right)$

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Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $- 262 ^ { \circ } 58 ^ { \prime }$

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Correct Answer
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Correct Answer
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Correct Answer
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Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

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Solve the problem. -The minute hand of a clock is 14 inches long. What distance does its tip move in 23 minutes? Give an exact answer.

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Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\sin \mathrm { s } = 0.8454$

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Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $86.9152 ^ { \circ }$

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Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }$ , where $t$ is time measured in seconds. Find the amplitude.

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Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sin 0.2721$

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Determine the equation of the graph. - $Determine the equation of the graph. - A) y = - \sec 2 x B) y = \sec \left( \frac { 1 } { 2 } x \right) C) y = \sec 2 x D) y = - \sec \left( \frac { 1 } { 2 } x \right)$

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Solve the problem. -A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

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Solve the problem. -A sensor light installed on the edge of a home can detect motion for a distance of $50 \mathrm { ft }$ . in front and with a range of motion of $238 ^ { \circ }$ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

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Solve the problem. -An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of $\frac { 1 } { 3 }$ radian has been covered, what is the linear speed of the object?

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Exam 6: The Circular Functions and Their Graphs

Find the exact circular function value. - cot⁡−11π6\cot \frac { - 11 \pi } { 6 }cot6−11π​

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Find the phase shift of the function. - y=cos⁡(x−π2) y = \cos \left( x - \frac { \pi } { 2 } \right) y=cos(x−2π​)

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Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - −262∘58′- 262 ^ { \circ } 58 ^ { \prime }−262∘58′

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The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find sin⁡θ\sin \thetasinθ .

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Solve the problem. -Let angle POQP O QPOQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQV R QVRQ are right angles. If θ=45∘\theta = 45 ^ { \circ }θ=45∘ , find the exact length of US.

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The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find csc⁡θ\csc \thetacscθ .

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Find the exact circular function value. - tan⁡7π6\tan \frac { 7 \pi } { 6 }tan67π​

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Solve the problem. -The minute hand of a clock is 14 inches long. What distance does its tip move in 23 minutes? Give an exact answer.

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Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - sin⁡s=0.8454\sin \mathrm { s } = 0.8454sins=0.8454

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Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 86.9152∘86.9152 ^ { \circ }86.9152∘

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Solve the problem. -The voltage E\mathrm { E }E in an electrical circuit is given by E=3.1cos⁡140πt\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }E=3.1cos140πt , where ttt is time measured in seconds. Find the amplitude.

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Use a table or a calculator to evaluate the function. Round to four decimal places. - sin⁡0.2721\sin 0.2721sin0.2721

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Determine the equation of the graph. -

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The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

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Solve the problem. -A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched 2ft2 \mathrm { ft }2ft and released. What is the equation for the resulting oscillatory motion?

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The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find cos⁡θ\cos \thetacosθ

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Solve the problem. -An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of 13\frac { 1 } { 3 }31​ radian has been covered, what is the linear speed of the object?

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Find the exact circular function value. - $\cot \frac { - 11 \pi } { 6 }$

Correct Answer
verified

Find the phase shift of the function. - $y = \cos \left( x - \frac { \pi } { 2 } \right)$

Correct Answer
verified

Correct Answer
verified

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $- 262 ^ { \circ } 58 ^ { \prime }$

Correct Answer
verified

Correct Answer
verified

Correct Answer
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Correct Answer
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Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

Correct Answer
verified

Correct Answer
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Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\sin \mathrm { s } = 0.8454$

Correct Answer
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Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $86.9152 ^ { \circ }$

Correct Answer
verified

Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }$ , where $t$ is time measured in seconds. Find the amplitude.

Correct Answer
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Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sin 0.2721$

Correct Answer
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Determine the equation of the graph. - $Determine the equation of the graph. - A) y = - \sec 2 x B) y = \sec \left( \frac { 1 } { 2 } x \right) C) y = \sec 2 x D) y = - \sec \left( \frac { 1 } { 2 } x \right)$

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Correct Answer
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Solve the problem. -A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Solve the problem. -An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of $\frac { 1 } { 3 }$ radian has been covered, what is the linear speed of the object?

Correct Answer
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