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: _________________________________________________________________
