Pre-Calculus

Pre-Calculus Name
Chapter 6 – Graphs of Trigonometric Functions Period

6.1 and 6.2 Supplementary Worksheet

6.1

1. 
   Change the degree measures to radian measures in terms of π.
   

a. 145° b.

2. 
   Change the radian measures to degree measures.
   

a. b. – 3.5
3. Use the unit circle to find the exact values. No Calculator!
a. sin ( – π ) b. cos

c. sin d. tan

e. sec 4π f. csc

g. cos h. sin

i. sin j. tan

k. cot l. sec

4. The radius of a circle is 9 inches. If a central angle measures , find the length of its intercepted arc.

Formula: .

5. The diameter of a circle is 24 inches. If a central angle measures 75º, find the length of its intercepted arc.



Formula: .
6. Find the area of a sector if the central angle measures radians and the radius of the circle is
10 centimeters.

Formula: .
7. Find the area of a sector if the central angle measures 82° and the diameter of the circle is
7.3 centimeters. Round answer to 3 decimal places.

8. If the area of a sector is 15 in² and its central angle is 0.2 radians, then find a) the radius of the circle and b) the arc length of the sector. Write answers in exact form.

6.2

9. Determine the angular velocity, w , of each situation. Formula: .

a. 1.8 revolutions in 9 seconds b. 250 revolutions in 32 minutes

10. Determine the linear velocity, v , of each situation. Formula: or .

a. w = 27.4 radians per second , r = 4 feet b. w = 200 revolutions in 160 seconds , r = 18 in

11. The diameter of a Ferris Wheel is 80 feet.

1. 
   If the Ferris Wheel makes one revolution every 45 seconds, then find the linear velocity of a person riding in the Ferris Wheel.
   

2. 
   Suppose the linear velocity of a person riding the Ferris Wheel is 8 ft/sec. What is the time for one revolution of the Ferris Wheel?