Chapter 7 Review

Section Topics What you should be able to do Measurement of Angles Find the measure of an angle in either degrees or radians 7-1 Find coterminal angles Sectors of Circles Find the arc length and area of a sector of a circle 7-2 Solve problems involving apparent size The Sine and Cosine Functions Use the definitions of sine and cosine to find values of these 7-3 functions Solve simple trigonometric equations Evaluating and Graphing Sine and Use reference angles, calculators or tables and special angles 7-4 Cosine to find values of the sine and cosine functions Sketch the graphs of these functions The other Trigonometric Functions Find values of tangent, cotangent, secant, and cosecant 7-5 functions Sketch the functions’ graphs 7-6 The Inverse Trigonometric Functions Find values of the inverse trigonometric functions

Converting degrees to radians:

Converting radians to degrees:

Converting decimal degrees to degrees/minutes/seconds:

Converting degrees/minutes/seconds to decimal degrees:

apparent size =

The 6 trigonometric functions:

The inverse functions:

Vocabulary you should know: Angle, initial ray, terminal ray, degree, minute, second, radian, standard position, coterminal angles, length of arc, area of a sector, sine & cosine functions, unit circle, circular function, reference angle, tangent & cotangent functions, secant & cosecant functions, Tan-1, Sin-1, Cos-1 Practice problems:

1. a. Convert -90 to radians. Give the answer in terms of . b. Convert 212 to radians. Give the answer to the nearest hundredth.

7p 2. a. Convert 3 radians to degrees. b. Convert 3.5 radians to degrees. Give the answer to the nearest minute or tenth of a degree.

3. Find two angles, one positive and one negative, that are coterminal with each given angle. a. -100 b. 320.3 7p c. 4 d. 22040’

4. A sector of a circle has radius 5 cm and central angle 137. Find its approximate arc length and area.

5. The sun is about 9 x 107 mi from Earth, and its apparent size is about .0043 radians. What is the sun’s approximate diameter?

6. Find sin and cos. a. b. c.

(- 3 , 1)

(-1, -1) (0, -1)

7. Complete each statement with one of the symbols <, >, or =. a. sin 70 ___ sin 65 b. cos 70 ___ cos 65 c. sin 313 ___ sin 314 d. cos 40 ___ cos 320 e. sin 30 ___ cos 60 d. cos 13 ___ sin 77

8. Give the exact value of each expression or state that the value is undefined. 5p 5p a. sin 6 b. cos (-180) c. sin 210 d. cos 6 2p e. tan (-) b. sec 3 c. cot (-60) d. csc 135

1 p 9. If cot x = - 3 where 2 < x < , find the values of the other five trigonometric functions

10. Give the exact value of each expression. a. Tan-1 ( - 3 ) b. sec (Sin-1 1 ) c. csc (Cos-1 (- 3 )) 3 2 5

11. To obtain the inverse cosine function, we restrict the domain of f (x) = cosx to 0 Ј x Ј p . Explain why this restriction is necessary.