Cogito
Trigonometry · Chapter 4 · Lesson 1
Inverse Trigonometric Functions
Going from a ratio back to an angle.
10 problems · about 20 minutes · F-TF.B.6, F-TF.B.7
What this lesson teaches
The student uses inverse trigonometric functions and explains why their domains are restricted.
- An inverse trigonometric function returns an angle.
- Its range is restricted so it gives exactly one answer.
- Other solutions exist, and a problem may need them.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Graphing Tangent: What is the period of y = tan(2x), in degrees?
Answer 90
Why 90°.
Review — Period and Phase Shift: y = cos(3x). What is the period, in degrees?
Answer 120
Why 120°.
Warm Up
Straightforward practice. Get the method working first.
4 problemssin θ = 0.5 and θ = 30°. What is the other solution below 360°?
Answer 150
Why 150°.
Why must arcsin have a restricted range?
Answer A function must give exactly one output.
Why Otherwise it would not be a function.
cos θ = 1. What is θ in degrees?
Answer 0
Why The point (1, 0).
cos θ = −1. What is θ in degrees?
Answer 180
Why The point (−1, 0).
Build It Up
The same ideas with more to keep track of.
2 problemssin θ = 0 and θ is between 0 and 360, not 0. What is θ?
Answer 180
Why y is zero there too.
Why is arcsin restricted?
Answer Otherwise one input would give many outputs.
Why A function needs one output.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Angle: sin θ = 1. What is θ, in degrees, between 0 and 360?
Answer 90 degrees
Why 90°.
The Second One: sin θ = 0.5 and θ = 30° is one answer. What is the other, between 0 and 360?
Answer 150 degrees
Why 150°.