Download Study Guide Chapter 4 Test

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Chapter 4 Test – Trigonometric Functions
Study Guide
Angle Measures
1. What is a radian? What does an angle with a measure of 1 radian look like?
2. How do you convert an angle measure from degrees to radians? From
radians to degrees?
Acute Angles
3. An acute angle in standard position will lie in which quadrant?
4. Given the location of a point in the first quadrant, how do you sketch the angle
and find all six trig functions related to that angle?
5. Given the measure of an acute angle, how do you sketch the angle and find
all six trig functions related to that angle?
6. In applied problems, how do you use trig ratios to solve for missing
information (side lengths, etc.)
7. When angles A and B are complementary, then cos(𝑎°) = sin⁡(𝑏°) and
cos(𝑏°) = sin⁡(𝑎°). Why?
All Angles
8. Given an angle measure in degrees or radians, how do you locate its position
on the unit circle?
9. What is a reference triangle? When are they used? What are the specific
ratios associated with 45° − 45° − 90° and 30° − 60° − 90° triangles?
10. In which quadrants is the value of cos⁡(𝜃) positive? In which quadrants is it
negative?
11. In which quadrants is the value of sin⁡(𝜃) positive? In which quadrants is it
negative?
12. In which quadrants is the value of tan⁡(𝜃) positive? In which quadrants is it
negative?
13. Given the value of a trig function, how do you determine in which quadrant it
is located? How do you determine the remaining trig ratios? (Ex. tan(𝜃) =
4
− 3)?
14. Given a point on the coordinate plane, how do you identify all 6 trig ratios for
the point?
15. For what values of 𝜃 are each of the 6 trig functions 0 or undefined?
Graphing Basic Trig Functions
16. What are the key points in the graphs of sin⁡(𝜃) and cos⁡(𝜃)? What do the
functions look like when they’re graphed?
17. How do you transform the graph of sin⁡(𝜃) or cos⁡(𝜃)?
a.
b.
c.
d.
e.
f.
How does the amplitude change?
What determines the vertical shift?
What determines the horizontal stretch?
What determines the horizontal translation?
How is the horizontal stretch related to the period of the function?
Given a graph of a transformed function, how do you determine the
domain and range shown in the graph?
g. Given a graph of a transformed function, can you determine the
equation that matches?
18. How do you find a trigonometric function that best models a given situation?
a. How do you find amplitude?
b. How do you find period?
c. How do you identify horizontal or vertical translations?
d. How do you identify the best shape of the graph (And which 4 are
easiest to choose from)?
e. How do you use those models to solve problems?
Inverse Trig Functions
19. Inverse trig functions enable you to find what?
20. How do you use a reference triangle to determine values of inverse trig
functions?
21. How do you evaluate inverse trig functions using the calculator?
22. In an applied problem, how do you use an inverse trig function to solve for an
angle measure?