Filters
Question type

Study Flashcards

Find the exact circular function value. - cot11π6\cot \frac { - 11 \pi } { 6 }


A) 32\frac { \sqrt { 3 } } { 2 }
B) 3\sqrt { 3 }
C) 32- \frac { \sqrt { 3 } } { 2 }
D) 3- \sqrt { 3 }

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

Correct Answer

verifed

verified

Find the phase shift of the function. - y=cos(xπ2) y = \cos \left( x - \frac { \pi } { 2 } \right)


A) π2\frac { \pi } { 2 } units up
B) π2\frac { \pi } { 2 } units to the right
C) π2\frac { \pi } { 2 } units to the left
D) π2\frac { \pi } { 2 } units down

E) C) and D)
F) All of the above

Correct Answer

verifed

verified

Solve the problem. -Ignoring friction, the time, tt (in seconds) , required for a block to slide down an inclined plane is given by the formula t=2bgsinθcosθt = \sqrt { \frac { 2 b } { g \sin \theta \cos \theta } } where bb is the length of the base in feet and g=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 4444 ^ { \circ } ? Round your answer to three decimal places.


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

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

Correct Answer

verifed

verified

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 26258- 262 ^ { \circ } 58 ^ { \prime }


A) 4.5696- 4.5696
B) 4.5596- 4.5596
C) 4.5796- 4.5796
D) 4.5896- 4.5896

E) A) and B)
F) None of the above

Correct Answer

verifed

verified

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 sinθ\sin \theta .  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 \theta .    A)   - \frac { 7 } { 24 }  B)   \frac { 7 } { 25 }  C)   \frac { 24 } { 25 }  D)   - \frac { 24 } { 25 }


A) 724- \frac { 7 } { 24 }
B) 725\frac { 7 } { 25 }
C) 2425\frac { 24 } { 25 }
D) 2425- \frac { 24 } { 25 }

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

Correct Answer

verifed

verified

Solve the problem. -Let angle POQP O Q be designated θ\theta . Angles PQRP Q R and VRQV R Q are right angles. If θ=45\theta = 45 ^ { \circ } , find the exact length of US.  Solve the problem. -Let angle  P O Q  be designated  \theta . Angles  P Q R  and  V R Q  are right angles. If  \theta = 45 ^ { \circ } , find the exact length of US.    A)   \frac { \sqrt { 2 } } { 2 }  B)  0 C)  1 D)   \sqrt { 2 }


A) 22\frac { \sqrt { 2 } } { 2 }
B) 0
C) 1
D) 2\sqrt { 2 }

E) A) and D)
F) None of the above

Correct Answer

verifed

verified

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 cscθ\csc \theta .  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 \theta .    A)   \frac { 25 } { 24 }  B)   - \frac { 25 } { 24 }  C)   - \frac { 25 } { 7 }  D)   \frac { 24 } { 7 }


A) 2524\frac { 25 } { 24 }
B) 2524- \frac { 25 } { 24 }
C) 257- \frac { 25 } { 7 }
D) 247\frac { 24 } { 7 }

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

Correct Answer

verifed

verified

Find the exact circular function value. - tan7π6\tan \frac { 7 \pi } { 6 }


A) 32\frac { \sqrt { 3 } } { 2 }
B) 33\frac { \sqrt { 3 } } { 3 }
C) 3- \sqrt { 3 }
D) 3\sqrt { 3 }

E) None of the above
F) A) and B)

Correct Answer

verifed

verified

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.


A) 16130πin\frac { 161 } { 30 } \pi \mathrm { in } .
B) 23840πin\frac { 23 } { 840 } \pi \mathrm { in } .
C) 23420πin\frac { 23 } { 420 } \pi \mathrm { in } .
D) 16115πin\frac { 161 } { 15 } \pi \mathrm { in } .

E) None of the above
F) A) and B)

Correct Answer

verifed

verified

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


A) 0.8657- 0.8657
B) 0.27590.2759
C) 1.00731.0073
D) 2.13432.1343

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

Correct Answer

verifed

verified

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 86.915286.9152 ^ { \circ }


A) 1.71701.7170
B) 1.51701.5170
C) 1.61701.6170
D) 1.81701.8170

E) All of the above
F) A) and D)

Correct Answer

verifed

verified

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


A) 3.13.1
B) 140
C) 6.26.2
D) 140π140 \pi

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

Correct Answer

verifed

verified

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


A) 0.96320.9632
B) 1.03821.0382
C) 0.26880.2688
D) 0.27900.2790

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

Correct Answer

verifed

verified

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)


A) y=sec2xy = - \sec 2 x
B) y=sec(12x) y = \sec \left( \frac { 1 } { 2 } x \right)
C) y=sec2xy = \sec 2 x
D) y=sec(12x) y = - \sec \left( \frac { 1 } { 2 } x \right)

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

Correct Answer

verifed

verified

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. - 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. -  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 )


A) y=2cos(3x) y = 2 \cos ( 3 x )
B) y=2cos(3x) y = - 2 \cos ( 3 x )
C) y=2cos(13x) y = - 2 \cos \left( \frac { 1 } { 3 } x \right)
D) y=2sin(3x) y = - 2 \sin ( 3 x )

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

Correct Answer

verifed

verified

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


A) s(t) =2sin6ts ( t ) = 2 \sin \sqrt { 6 } t
B) s(t) =12sin112ts ( t ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 12 } } t
C) s(t) =2sin16ts ( t ) = 2 \sin \sqrt { \frac { 1 } { 6 } } t
D) s(t) =6sin2ts ( t ) = 6 \sin \sqrt { 2 } t

E) None of the above
F) All of the above

Correct Answer

verifed

verified

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 cosθ\cos \theta  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 \theta     A)   \frac { 7 } { 25 }  B)   \frac { 7 } { 24 }  C)   - \frac { 7 } { 25 }  D)   - \frac { 24 } { 25 }


A) 725\frac { 7 } { 25 }
B) 724\frac { 7 } { 24 }
C) 725- \frac { 7 } { 25 }
D) 2425- \frac { 24 } { 25 }

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

Correct Answer

verifed

verified

Solve the problem. -The minimum length LL of a highway sag curve can be computed by L=(θ2θ1) S2200( h+Stanα) \mathrm { L } = \frac { \left( \theta _ { 2 } - \theta _ { 1 } \right) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } \tan \alpha ) ^ { \prime } } where θ1\theta _ { 1 } is the downhill grade in degrees (θ1<0) ,θ2\left( \theta _ { 1 } < 0 ^ { \circ } \right) , \theta _ { 2 } is the uphill grade in degrees (θ2>0) ,S\left( \theta _ { 2 } > 0 ^ { \circ } \right) , \mathrm { S } is the safe stopping distance for a given speed limit, hh is the height of the headlights, and α\alpha is the alignment of the headlights in degrees. Compute LL for a 55 -mph speed limit, where h=1.6fth = 1.6 \mathrm { ft } , α=0.8,θ1=5,θ2=1\alpha = 0.8 ^ { \circ } , \theta _ { 1 } = - 5 ^ { \circ } , \theta _ { 2 } = 1 ^ { \circ } , and S=336ftS = 336 \mathrm { ft } . Round your answer to the nearest foot.


A) 525ft525 \mathrm { ft }
B) 553ft553 \mathrm { ft }
C) 568ft568 \mathrm { ft }
D) 538ft538 \mathrm { ft }

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

Correct Answer

verifed

verified

Solve the problem. -A sensor light installed on the edge of a home can detect motion for a distance of 50ft50 \mathrm { ft } . in front and with a range of motion of 238238 ^ { \circ } . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.


A) 5192.35ft25192.35 \mathrm { ft } ^ { 2 }
B) 10,384.81ft210,384.81 \mathrm { ft } ^ { 2 }
C) 10,384.71ft210,384.71 \mathrm { ft } ^ { 2 }
D) 5192.25ft25192.25 \mathrm { ft } ^ { 2 }

E) None of the above
F) A) and B)

Correct Answer

verifed

verified

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 } radian has been covered, what is the linear speed of the object?


A) 3827 cm\frac { 38 } { 27 } \mathrm {~cm} per sec
B) 1927 cm\frac { 19 } { 27 } \mathrm {~cm} per sec
C) 19 cm19 \mathrm {~cm} per sec
D) 57 cm57 \mathrm {~cm} per sec

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

Correct Answer

verifed

verified

Showing 241 - 260 of 289

Related Exams

Show Answer