Trigonometric Identities Worksheet - GMU Math [PDF]

Trigonometric Identities Worksheet

Introduction to Identities 1. If sin  

3 , then csc  ? 5

2. If cos   

3 , then sec  ? 2

3. If tan   2 , then cot   ?

4. If sec  1 , then cos   ?

5. If sin   

6. If sin  

3 4 and cos   , find tan  and cot  . 5 5

3 and  terminates in quadrant II, find cos  . 5

7. Write sec tan  in terms of sin  and cos  and then simplify.

8. Add

1 1  . sin  cos 

9. Multiply (sin   2)(sin   5) .

Proving Identities 1. Prove sin  cot   cos .

2. Prove tan x  cos x  sin x(sec x  cot x) .

sin 2  3. Prove1  cos   . 1  cos 

4. Prove tan x  cot x  sec x csc x.

Sum and Difference Formulas 1. Find the exact value for cos 75

2. Show that cos( x  2 )  cos x .

3. Write cos3x cos 2 x  sin 3x sin 2x as a single cosine.

4. If sin A 

3 5 with A in QI and cos B   with B in QIII, find 5 13

(a) sin( A  B)

(b) cos( A  B)

(c) tan( A  B)

Double-Angle and Half-Angle Formulas 1. If sin A 

3 with A in QII, find sin 2A . 5

2. Prove (sin   cos  )2  1  sin 2 .

3. If sin A 

1 , find cos 2A . 5

4. If sin A  

12 and 180  A  270 , find 13

 A  2

(a) sin 

 A  2

(b) cos 

Trigonometric Equations 1. Find all values of x for which 2 cos x  3  0 , if 0  x  360 .

2. Solve 2 sin   3  0 , if 0  x  360 .

3. Solve 2 cos2 t  9cos t  5 , if 0  t  2 .

4. Solve 2 sin 2   2sin  1  0 , if 0    2 .

5. Solve cos 2  3sin   2  0, if 0    360 .

 A  2

(c) tan 