Math 121 Exam

Evaluate the expression without using a calculator, and write your answer in radians. Do not round. tan-1⁡(-1)=

- pi over 4

Evaluate the expression without using a calculator, and write your answer in radians. Do not round. arctan⁡(- square root 3 over 3 )=

- pi over 6

Use the unit circle and the fact that cosine is an even function to find the following. Answer exactly. cos⁡(-210°)=

- square root 3 over 2

Let sin⁡A=-4/5 with A in Q4 and find sin(2A)

-.96

Use the unit circle to evaluate the function. Answer exactly. tan⁡(3⁢pi/4)=

-1

If cos⁡(A)=-12 with A in Q3, then cos (A/2) =

-1/2

Use a calculator to find the following. Round to 4 decimal places.cot⁡(176°10′)=

-14.9244

If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation theta, then the height ℎ of the projectile at time t is given byℎ=-16⁢t2+vt⁢sin⁡(theta)Give the equation for the height, if v is 500 feet per second and theta is 30°.

-16t2 +500t *.5

Use half-angle formulas to find exact values for tan (165)

-2 + square root 3

Let sin⁡A=-45 with A in Q3 and find tan(2A)

-3.43

Find the exact value of the following. cos⁡(135°)=

-square root 2 over 2

A Ferris Wheel has diameter of 179 feet and one complete revolution takes 17 minutes. Find the linear velocity of a person riding on the wheel. Give your answer in miles per hour and round to the nearest hundredth.

.38 mi/hr

Calculate the exact value of the expression using sum and differences. Do not use a calculator. cos⁡(15°)⁢cos⁡(75°)+sin⁡(15°)⁢sin⁡(75°)=

.5

Evaluate the expression without using a calculator, and write your answer in radians. Do not round. sin-1⁡(0)=

0

For the pair of vectors, find u dot v u = i-j v=-i-j

0

Calculate the exact value of the expression using sum and differences. Do not use a calculator. cos⁡(15°)⁢cos⁡(75°)-sin⁡(15°)⁢sin⁡(75°)

0 muthuhfudgkuh

Find the exact value of the following. tan⁡(210°)=

1 over square root 3

Evaluate without using a calculator. Answer exactly. sec ⁡( tan-1 ⁡(3/4) )=

1.25

If cos⁡(A)=12 with A in Q1, then Sin(A/2) =

1/2

Write the following in terms of sin⁡(x) and cos⁡(x), and then simplify if possible. Leave your answer in terms of sines and cosines only.sec⁡(x)⁢csc⁡(x)⁢cot⁡(x)=

1/sin squared of x

Write the following in terms of sin⁡(x) and cos⁡(x), and then simplify if possible. Leave your answer in terms of sines and cosines only. sec⁡(x)⁢cot⁡(x)=

1/sinx

Use the quadratic formula to find all degree solutions. Enter as a list, assume it is of the form "A°+360∘⁢k". Use a calculator to approximate all answers to the nearest tenth of a degree.2⁢sin2⁡(theta)-1=-5⁢sin⁡(theta)

10.7 + 360 k 169.3 + 360 k

An equilateral triangle has an altitude of 9.8 inches. Find the length of the sides rounded to at least 1 decimal place.

11.3 inches

A gasoline-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the blade is traveling at 1200 feet per second. Through how many revolutions per minute is the blade turning? Answer exactly in terms of pi or round to the nearest whole number.

11459.16 rpm

From a point on the ground, a person notices that a 104-foot antenna on the top of a hill subtends an angle of 2°. If the angle of elevation to the bottom of the antenna is 27°, find the height of the hill.

1183.3

Let sin⁡A=-5/13 with A in Q3 and find COT(2A)

119 over 120

For the equation,2⁢cos2⁡(theta)+11⁢cos⁡(theta)=-5 Solve for all degree solutions in ascending order.

120 + 360 k and 240 + 360 k

For the equation,(2⁢cos⁡(theta)+3)⁢(2⁢cos⁡(theta)+1)=0 Solve for all degree solutions in ascending order.

120+ 360 k and 150 + 360 k and 210 + 360 k and 240 + 360 k

For the equation,2⁢tan⁡(theta)+2=0 Solve for all degree solutions.

135 + 180 k

Find the angular velocity, in radians per minute, associated with the given revolutions per minute (rpm). Answer exactly, in radians per minute, in terms of pi or round to at least 2 decimal places. 25 2/3 rpm=

161.27 rad/min

Find exact values for the following. no calculator tan(75)

2 + square root 3

Point p sweeps out central angle theta as it rotates on a circle of radius r as given below. Find the angular speed of point p in radians per second. theta=4⁢pi radians , t=2⁢pi sec detail solution in 3.5

2 rad / sec

The minute hand of a clock is 2.1 centimeters long. How far does the tip of the minute hand travel in 10 minutes? Answer exactly or round to 2 decimal places.

2.20 cm

The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 7 feet and the angle through which it swings is 20°, how far does the tip of the pendulum travel in 1 second? Answer exactly or round to 1 decimal place.

2.4 ft

Use the quadratic formula to find all degree solutions. Use a calculator to approximate all answers to the nearest tenth of a degree and between 0 and 360 degrees.2⁢sin2⁡(theta)+5⁢sin⁡(theta)-2=0

20.5 + 360 k and 159.5 + 360 k

Find the angular velocity, in radians per minute, associated with the given revolutions per minute (rpm). Answer exactly, in radians per minute, in terms of pi or round to at least 2 decimal places. 3.6 rpm=

22.62 rad/min

A lawn sprinkler is located at the edge of a lawn. The sprinkler is set to rotate through 180° and project water out 40 feet. What is the area the lawn watered by the sprinkler? Answer exactly or round to the nearest square foot.

2513 ft2

A cannonball is fired in the air at an angle of 45°. How far does it travel before it is 1,900 feet above ground? (Assume the cannonball travels in a straight line. Ignore the force of gravity and wind resistance. Round your answer to the nearest foot.)

2687 ft

A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depressions from his balloon to a friend's car in the parking lot is 35°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36°. At that time, what is the distance between him and his friend? (Round to the nearest foot.)

273

Give the number of significant digits in the following number. 92.3

3

Evaluate without using a calculator. Answer exactly. cos⁡(cos-1⁡ (3/4) )=

3/4

Evaluate without using a calculator. Answer exactly. tan⁡ (sin-1 ⁡(3/5) )=

3/4 or .75

Find the following dot product: <6,4> dot <3,3>

30

How long should an escalator be if it is to make an angle of 31° with the floor and carry people a vertical distance of 18 feet between floors? Round to at least 1 decimal place.

34.9 ft

Convert the following to degrees and minutes. 35.75°

35 degrees 45 minutes

Evaluate without using a calculator. Answer exactly. cot⁡ (tan-1 ⁡(3/4) )=

4/3

A 74.6-foot rope from the top of a circus tent pole is anchored to the ground 49.7 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.) Round to at least 1 decimal place.

41.8 degrees

Find the magnitude of the following vector. Answer exactly. 3i - 4j

5

Give the number of significant digits in the following number. 8.5082

5

Let csc⁡A=square root 5 with A in Q1 and find sec(2A)

5/3

A 54-foot wire running from the top of the tent pole to the ground makes an angle of 55° with the ground. If the length of the tent pole is 48 feet, how far is it from the bottom of the tent pole to where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground. Just give one of the answers rounded to the nearest whole number.)

50

Name the reference angle for 232°10′.

52 degrees 10 min

Name the reference angle for -120°.

60

For the equation, 2 ⁢cos ⁡theta = 1 Solve for all degree solutions.

60 + 360 k and 300 + 360 k

A space shuttle 275 miles above the earth is orbiting the earth once every 4 hours. How far does the shuttle travel in 1 hour? (Assume the radius of the earth is 4,000 miles.) Answer exactly or round to the nearest mile.

6715 mi

Add or subtract as indicated. (40°49′)+(27°39′)=

68 degrees 28 min

Mark pulls his two children in a wagon by exerting a force of 25 pounds on the handle at an angle of 30 degrees with the horizontal. How much force is done by mark while pulling the wagon by 350 feet?!?!?!?!

7,578 ft-lb

A cable car travels by clamping onto a steel cable that circulates in a channel beneath the streets. The cable is driven by a large 12-foot-diameter pulley, called a sheave. The sheave turns at a rate of 17 revolutions per minute. Find the speed of the cable car, in miles per hour, by determining the linear velocity of the cable (rounded to the nearest hundredth of a mile).

7.28 mi/hr

Convert the following to degrees and minutes. 71.5 degrees

71 degrees 30 min

Find the distance s covered by a point moving with linear velocity v for a time t if:v=15 feet/second and t=5 seconds s= (use da formula) also detailed soultions 3.5

75 ft

A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is 51°. He then walks 72 feet further away and observes that the angle of elevation to the top of the antenna is 30°. Find the height of the antenna to the nearest foot.

78

Find the area of the sector formed by central angle theta in a circle of radius r. Answer exactly. theta=4 radians; r=7 cm

98 cm2

For the pair of vectors, find 2u - 3v u = <3,5> v = <-5,5>

<21, -5>

The following problems refer to triangle ABC. Solve it. Round angles to the nearest whole number and sides to 2 decimal places. a=0.67, b=0.88, c=0.52

A = 49.4 B = 94.5 C = 36.1 a = .67 b = .88 c = .52

The following problem refers to triangle ABC, find all missing parts. Round degrees to 1 decimal places and sides to the nearest whole number.B=68.9° , C=81.8° , c=249 inches

A= 29.3 B= 68.9 C= 81.8 a= 123.1 b= 234.7 c= 249

Vector v is in standard position, and makes an angle of 30° with the positive x-axis. Its magnitude is 26. Write v in component form 〈a,b〉 and using standard unit vectors ai+bj. Round to 2 significant figures

Component form: <23,13> Standard Unit form: 23i + 13j

A plane travels 170 miles on a bearing of N46°E, and then changes its course to N25°E and travels another 140 miles. Find the total distance traveled north and the total distance traveled east. Round to the nearest whole number.

East: 181.5 miles North: 245 miles

The two equal sides of an isosceles triangle are each 31 centimeters. If the base measures 16 centimeters, find the height and the measure of the two equal angles rounded to the nearest whole number.

Height: 30 cm Two Equal Angles: 75 degrees

A bullet is fired into the air with an initial velocity of 1,200 feet per second at an angle of 50° from the horizontal. Find the magnitudes of the horizontal and vertical components of the velocity vector. Round to nearest whole number. Find the total horizontal distance traveled by the bullet in 5 seconds using your rounded answer for the horizontal velocity.

Horizontal Velocity: 771.3 fps Vertical Velocity: 919.3 fps Find the total horizontal distance traveled by the bullet in 5 seconds: 3856.5 ft

The following problems refer to triangle ABC. Round your answer to the nearest whole number.If a=29 , b=28 , c=30 , find the largest angle.

Largest Angle: 63

Find the magnitude of the vector and the angle theta that the vector makes with the positive x-axis, where 0°≤ theta <360°. Answer exactly. u= i-square root 3⁢j

Magnitude: 2 Angle: 300

For the equation, identify the amplitude, period, and phase shift and sketch (at least) one complete cycle of the graph .y=sin⁡(2⁢x-pi) period: Amplitude: Phase Shift:

Period: pi Amplitude: 1 Phase Shift: pi over 2

Let sin⁡A=-4/5 with A in QIII and sin⁡B=-12/13 with B in QIII. Answer exactly. Sin(A+B)= Cos(A+B) = Tan(A+B) =

Sin(A+B)= 56/65 Cos(A+B)= -33/65 TAN(A+B) = -56/33

The earth rotates through one complete revolution every 24 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 24 hours. Find the angular and linear velocity of a person standing on the equator. The radius of earth is approximately 4000 miles. Answer the angular velocity exactly in radians per hour. W= Answer the linear velocity, in miles per hour, exactly or rounded to the nearest whole number. V=

W= 2pi rad/24hr V= 1047.20mi/hr

The following problem refers to triangle ABC. Round your answer to the nearest whole number.If B=70° , C=50° , and c=14 cm, find b.

b = 17 cm

The following problems refer to triangle ABC. Round your answer to the nearest whole number. If a=139 , b=78 , C=60° , find c.

c = 121

Find the third side to the following non-right triangle (there are two possible answers). Round to the nearest foot. A = 48, a = 49ft , b= 51ft

c=65ft, 3 ft

Write each expression as a single trigonometric function. cos⁡(3⁢x)⁢cos⁡(7⁢x)+sin⁡(3⁢x)⁢sin⁡(7⁢x)=

cos(-4x)

A ship travels 158 km on a bearing of S54°E. How far east and how far south has it traveled? Round to the nearest whole number. detailed solution on 2.5

east: 127.9 km South: 92.9 km

Find the third side to the following non-right triangle. Round to the nearest whole number. A = 113, a = 48m , b = 61 m

no solution

For the equation, identify the amplitude, period, and phase shift and sketch (at least) one complete cycle of the graph. y=cos⁡(2⁢x-pi over 2) period: Amplitude: Phase Shift:

period: pi Amplitude: 1 Phase Shift: pi over 4

Evaluate the expression without using a calculator, and write your answer in radians. Do not round sin-1⁡(square root 3 over 2)=

pi over 3

Evaluate the expression without using a calculator, and write your answer in radians. Do not round. arcsin⁡(square root 2 over 2)=

pi over 4

For the problem below, theta is a central angle that cuts off an arc of length s. Find the radius r of the circle. theta=4 radians; s=20 feet

r = 5 ft

For the problem below, theta is a central angle in a circle of radius r. Find the length of arc s cut off by theta. theta=3 radians; r=6 inches

s = 18 inches

Find the distance s covered by a point moving with linear speed v for a time t if: v=51 mi/hr and t=1/2 hr

s = 25.5 mi

Find all six trigonometric functions of theta if the given point is on the terminal side of theta. Answer exactly. (-3,4)

sin .8 cos -.6 tan -4/3 cot -3/4 sec -5/3 csc 1.25

Find all six trigonometric ratios of theta if sec⁡(theta)=2 and theta terminates in QI. Round to 2 decimal places.

sin .87 cos .5 tan 1.73 cot .58 sec 2 csc 1.15

Write each expression as a single trigonometric function. sin⁡(8⁢x)⁢cos⁡(7⁢x)+cos⁡(8⁢x)⁢sin⁡(7⁢x)=

sin(15x)

Which of the following is a pythagorean identity?

sin2+cos2 = 1

Write sin⁡(x) in terms of cos⁡(x) only .functions, just answer the multiple choice portion appropriately.

square root 1 - cos squared of x

Find the magnitude of the following vector. Answer exactly. <-3,-1>

square root 10

Find exact values for the following. no calculatr sin(5pi pver12)

square root 2 + square root 6 over 4 (both over 4)

Use the unit circle to evaluate the function. Answer exactly. cot⁡(210°)=

square root 3

If sin⁡(A)=4/5 with A in Q2, then CSC(A/2) =

square root 5 over 2

Find exact values for the following. no calculator sin(75)

square root 6 + square root 2 over 4 (both over 4)

Find exact values for the following. no calculator cos(75)

square root 6 over 4 - square root 2 over 4

If sin⁡(A)=-4/5 and 270°<theta<360°, find sin⁡(A/2). Answer exactly.

square root 8 over 10

Find the angle theta between the given vectors, where 0°≤ theta ≤180°. Round to 1 decimal place, if necessary u = 5i+7j v= 2i + 5j

theta = 13.7

Find theta, if 0°<theta<360° and sin⁡(theta)= square root 2 over 2 with theta in QII.

theta = 135

Find the angle theta between the given vectors, where 0°≤ theta ≤180°. Round to 1 decimal place, if necessary. u = -3j, v = -2i

theta = 90

Find the linear velocity v of a point moving with uniform circular motion, if the point covers a distance s in an amount of time t, where: s=9 ft and t=3 min detail solution in 3.5

v= 3 ft/min