# Homework Assignment 7.3

Class Section

Homework Assignment 7.3

18 points

Print out this assignment and write your name on it and turn it in instead of answering the

questions on notebook paper. You may print front and back if you wish. Be sure to include your

first name and last name. Put your class section number on the area of the line above “Class

Section”.

Problems 1 – 6: Find the function f (x) that will make the given equation an identity. The

function f (x) may be a trig function, algebraic function, or constant function.

Each problem has a solution. Simplify all answers.

1.

cos(2x)

= f 2(x)

1 – tan2(x)

2.

f (x) = _______________________

3.

cos2(x)

1 – 1 + sin(x) = f (x)

1 + cos(2x)

= f (x)

sin(2x)

f (x) = _______________________

cos(x)

= f (x)

1 + sin(x)

f (x) = __________________________

4.

f (x) = _______________________

5.

tan(x) +

x

x

tan + cot = 2 f ( x)

2

2

f (x) = ___________________________

6.

cos(x)

1 + sin(x)

+

= 2f (x)

1 + sin(x)

cos(x)

f (x) = ___________________________

Problems 7 – 11: Verify each identity. Provide all necessary details.

7.

sec2(θ) csc2(θ) = sec2(θ) + csc2(θ)

8.

cos(2θ)

= cos(θ) – sin(θ)

cos(θ) + sin(θ)

9.

tan(θ )

θ

tan =

2 sec(θ ) + 1

10. sin(2θ) =

2 tan(θ)

1 + tan2(θ)

11. sin(2x) – tan(x) = tan(x) cos(2x)

Problems 12 – 14:

Show that each of the following is not an identity.

12. cos(2θ) = 2cos(θ) sin(θ)

t sin(t )

13. sin =

2

2

14. cos(2t) = 2cos(t)

Problems 15 and 16: Write each of the following as a product of trig functions. Simplify your

answers.

15. sin(6θ) + sin(3θ)

Answer: _________________________________________________________________

16. cos(5θ) – cos(θ)

Answer: __________________________________________________________________

Problems 17 and 18: Write each of the following as a sum or difference of trig functions.

Simplify your answers.

17. sin(6θ) sin(3θ)

Answer: _________________________________________________________________

18. cos(5θ) cos(θ)

Answer: _________________________________________________________________