The document is a trigonometry study guide that provides definitions, formulas, identities, and questions about trigonometric functions including inverse trig functions, the unit circle, graphs of trig functions, and verifying trigonometric identities. It covers topics like inverse functions, reciprocals, the unit circle, laws of sines and cosines, trig function definitions, graphing trig functions, and verifying identities. The study guide provides information and questions to help students review important concepts in trigonometry.

1. Precalculus
Trig Study Guide
1. The inverse of the cosine function is the _______________________ relation.
(Know all inverses)
2. The reciprocal of the sine function is the ______________________ function.
(Know all reciprocals)
3. The unit circle has a radius of _________________.
4. The Law of Sines is: __________________________________________
5. The Law of Cosines is: ______________________________________________
6. SOHCATOA means: ________________________________________________
7. The Pythagorean Identity is: __________________________________________
8. Trig functions use angles to determine __________ _______________________.
9. Inverse Trig relations use side lengths to determine _______________________.
10. The Laws of Sines and Cosines can be used to solve triangles that are not
____________________ triangles.
Draw the 2 standard triangles that are used to derive the Unit Circle and label the angles
and side lengths.
11. (45, 45, 90) 12. (30, 60, 90)
13. Name the Double-Angle Identity for sin 2θ = _____________________________
14. Give the Half-Angle Identity for cos
a
/2 = _______________________________
15. a) (Below) graph y = sin x
b) The period is ____________________________________________________
c) The domain is ___________________________________________________
d) The range is _____________________________________________________
e) The x-intercepts are _______________________________________________
f) The y-intercept is _________________________________________________
g) The maximum values are y = ________________ when x = _______________
h) The minimum values are y = ________________ when x = _______________

2. 16. y = 4 cos (
x
/2 + π) – 6
a) Midline: __________________________________________________
b) Amplitude: ________________________________________________
c) Period: ___________________________________________________
d) Phase Shift: _______________________________________________
e) Graph:
17. The period of both y = tan kx and y = cot kx is ____________________________
18. y = csc (
x
/2 -
π
/4) + 2
a) Midline: __________________________________________________
b) Amplitude: ________________________________________________
c) Period: ___________________________________________________
d) Phase Shift: _______________________________________________
e) Graph:
19. Verify that sec2
x – tan x cot x = tan2
x is an identity.