MATH 1550 Algebra Questions

MATH 1550, Spring 2022Test 3
Show all of your work to recieve full credit. Calculators are not permitted on this exam.
1. Verify the following identity.
sin (2x) tan (x) +
1
1
−
= 3 − 2 cos2 (x)
2
cos (x) cot2 (x)
1
2. Evaluate the following expression exactly:
cos
−1

 
4π
cos
3
3. Use a sum or difference identity to find the exact value of:

7π
tan −
12
2

4. Use a half-angle identity to find the exact value of:
sin (112.5◦ )
5. Evaluate the following trigonometric functions exactly:
(a) sec
3π
4


(b) tan(210◦ )
(c) sin − 5π
3


3
(d) cos(300◦ )
(e) csc − 7π
6


(f) cot(−315◦ )
6. Use the given triangle to find the values of:
(a) sin θ
(b) cos θ
(c) tan θ
(d) sec θ
(e) csc θ
(f) cot θ
4
7. Write an equation for the function represented in the following graph.
8. State the amplitude and period of the following function, and then graph the function.
 
1
x
y = −3 cos
2
5
9. Find all solutions to the following trigonometric equations:
(a) cos (2θ) + cos θ = 0
(b) 2 sec2 θ + tan2 θ = 3
6