Precalculus

Name: __________ _

Date: ____ _

1. Find the complement and supplement of an angle that measures 57·

2. Convert the following angles

a. 120· to radians

b. S;r radians to degrees 2

3. Find the radian measure of the central angle of the circle of radius 5 meters that intercepts an

arc of length 22 meters.

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4. The circular blade of a saw has a diameter of 7 inches and rotates at 4600 revolutions per

minute.

a. Find the linear speed of the saw teeth in feet per second. Round your answer to two

decimal places.

b. Find the angular speed of the blade in radians per second

5. Find the value of the six trigonometric functions of the angle B

/1 / t

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// //

/\e d

2

4

6. A 45-meter line is used to tether a helium-filled balloon. Because of a breeze, the line makes an

angle of approximately 65 ° with the ground. What is the height of the balloon? Round your

answer to two decimals.

1

7. A biologist wants to know the width w of a river. From point A, the Dtotogtsr watKs uuwti=>LI ~:a•••

93 feet to point B and sights to point C (see figure). From this sighting, it is determined that

(} = 46°. How wide is the river? Round your answer to two decimals.

A B

6 8. If sin ( (}) = -- and (} lies in Quadrant 4, find cos(} and tan(}

7

1

9. Graph Sketch the graph of the function below, being sure to include at least one full period.

y- cos( x+ 3:)

! : i : ' i f----L---+--+~~-+---+-~~, --, ~; ----: -~---~--------~

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10. Find the exact value of cos (sin -I ~).

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ii t----1

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Extra Credit:

A certain satellite orbits x = 11,700 miles above Earth's surface (see figure). Find the angle of depression a from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

NotiJ.rtN-'Il r,, s.:klc

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x mt -, GPS ---------------- ~ :.-: "'Y satellite

- -- - - - -. ) ---~ _ - · Alh1le of '

.~- ~ , I

depre<;ston 1