PAP Pre-Calc
Trig Test #2(1)
Block:
Name:
Section 1 No calculator allowed
There are nine Pythagorean Identities. What are they?
1.
4.
7.
2.
5.
8.
3.
6.
9.
𝜋
10. What is an identity for sin (𝑥 − 2 )?
11. What is an identity for cos(−𝑥)?
12. What is an identity for sin(−𝑥)?
13. What is an identity for cos (𝑥 − 2 )?
𝜋
3𝜋
𝜋
14. What is an identity for sin ( 2 − 𝑥)?
1
16. 𝐶𝑜𝑠 −1 (− 2) =
19. sec
2𝜋
3
17. sin
5𝜋
3
18. 𝑇𝑎𝑛−1 (−√3) =
=
21. 𝐶𝑜𝑡 −1 (−1) =
20. 𝐴𝑟𝑐𝑆𝑖𝑛(1) =
=
23. 𝐶𝑠𝑐 −1 (−
22. cot 𝜋 =
25. 𝑐𝑜𝑠 [𝑇𝑎𝑛−1 (−
15. What is an identity for cos ( 2 − 𝑥)?
√3
)]
3
2√3
)
3
=
24. csc 𝜋 =
26. 𝑠𝑒𝑐 [𝑆𝑖𝑛−1 (−
√3
)]
2
Section 2 No calculator allowed
Graph one period of the following. Show all x and y scale.
𝜋
2
1. 𝑦 = 3 cos (𝑥 − 6) + 11
3
4. 𝑦 = − 4 sin(3𝑥 − 6)
2. 𝑦 = sin 4𝑥
𝜋
5. 𝑦 = −5 cos ( 2 𝑥)
7. There is a max point at (5,2) and a min point at (-7,-10)
a) Write the equation of a sine wave through those points.
b) Write the equation of a cosine wave through those points.
8. Graph the following in radians on
the grid to scale.
A.
1
2
𝑦 = −4 sin ( 𝑥 + 7) + 10
𝜋
B. 𝑦 = 6 cos 6 (𝑥 − 4) + 3
1
C. 𝑦 = tan 4 (𝑥 + 12) − 8
D. 𝑦 = −5 sec(2𝑥 − 16) + 14
3. 𝑦 = tan 3𝑥
6. 𝑦 = 3 − sin(6𝑥)
Section 3 Calculator allowed
Simplify the following as far as possible. Just give me the answer. You may use scratch paper or a marker for more
space.
1.
4.
7.
sin 𝑥
𝑐𝑜𝑠 𝑥
1
cos 𝑥
sin 𝑥
cos 𝑥
2.
+
cos 𝑥
5.
sin 𝑥
tan 𝑥+sin 𝑥
8.
sec 𝑥+1
sec 𝑥
3.
tan 𝑥
𝑐𝑜𝑠 2 𝑥
1−sin 𝑥
𝑠𝑖𝑛2 𝑥
1−cos 𝑥
−1
− cos 𝑥
6.
1−𝑠𝑖𝑛2 𝑥
𝑐𝑠𝑐 2 𝑥−1
𝑡𝑎𝑛2 𝑥𝑠𝑒𝑐 2 𝑥 − 𝑡𝑎𝑛2 𝑥
9. (4 sin x  3 cos x) 2  (3 sin x  4 cos x) 2
Solve the following for x between 0 ≤ 𝑥 ≤ 2𝜋
10. 2𝑠𝑖𝑛2 𝑥 + sin 𝑥 − 1 = 0
13. 2 cos 𝑥 + √3 = 0
11. 𝑡𝑎𝑛2 𝑥 − 1
12.
14. −3 csc 3 𝑥 + 12𝑐𝑠𝑐 2 𝑥 − 7 csc 𝑥 + 1 = 0
15.
3𝑐𝑜𝑠 2 𝑥 − 5 cos 𝑥 − 7 = 0
3𝑠𝑒𝑐 2 𝑥 − 5 sec 𝑥 − 7 = 0
Use your calculator to assist in evaluating the following trig functions. Do everything in radians.
16. 𝑆𝑖𝑛−1 (4)
17. sin(4)
18. 𝑇𝑎𝑛−1 (4)
19. tan(4)
20. 𝐶𝑠𝑐 −1 (4)
22. Question #16 is using trig symbols to ask a question. Ask that question in words.
23. Question #17 is using trig symbols to ask a question. Ask that question in words.
21. sec(4)