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The following will guide you through the high points of a trigonometry review. Parts I and II will be answered with the help of the computer. Use any reference sources you can find if you need help with Part III.
 

part I
 
 

     Display the graph to help with the following exercise.
 

Fill in the unit circle below with the sine and cosine values for the angles 0 ,pi/6,pi/4, pi/3 , pi/2 and all other angles in which have these angles as reference angles.     Hint
 

For example, label the points as follows  and 

part II
 

The period of a function is defined to be a value k such that f ( + k ) = f () for all .
 

1.     Display the graph used in the following problems.  Determine the period of each of the functions below

    a. sine

    b. cosine

    c. tangent
 

2. Determine whether the graphs have even or odd symmetry

    a. y = sin 

    b. y = cos 

    c. y = tan 
 

3. Graph y = sin (   + ) and y = cos () .

    a. Is there any difference between the graphs of these two equations?

    b. Explain what caused this.
 

4. Consider the function y = tan .

    a. Why does it have vertical asymptotes?

    b. What are the values of in the interval  where these occur?
 
 

Part III
 
 

1. Define the following trigonometric functions as the ratios of the sides O (Opposite), A (Adjacent), and H (Hypotenuse) of a right triangle.

    a. sin  =

    b. cos =

    c. tan  =
 

2. Define the following in terms of the elementary trigonometric functions.

Note that sine and cosine are called elementary trigonometric functions.

    a. tan =

    b. sec =

    c. csc  =

    d. cot  =

    e. sin () =

    f. cos () =
 

3. Using the Pythagorean identity sin² + cos²  = 1 derive the following.

    a. tan²+ ____   =____

Hint:Divide by cos².

    b. ____  + cot²  = _____

Hint:Divide by sin².
 

4. Fill in the blanks for the sum identities below.

    a. sin (x + y ) =

    b. cos (x + y ) =
 

5. Use Q.4a and Q.4b to derive the double angle identities below.

    a. sin 2  =

    b. cos 2 =
 

6. Solve the equations below simultaneously to obtain the half angle identities for cos² and sin².

    a. cos²=

    b. sin²=
 

7. Find the missing angle and missing lengths (correct to the nearest hundredth) in the triangle below.

8. Find each of the following (use exact values--no approximations)

    a. sin () =
    b. tan  =
    c. cos () =
    d. cos () =
 

9. Solve the following equations in the interval 

    a. tan x = -1

    b. sec x = 2

    c. sin x = -1

    d. cos x = 
 

10. Where does sin x = cos x on the interval ?
 

11. Solve the equation sin 2x + sinx = 0 for x.