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Cogito

Trigonometry · Chapter 4 · Lesson 1

Practice Worksheet

Inverse Trigonometric Functions

Going from a ratio back to an angle.

10 problems · about 20 minutes · F-TF.B.6, F-TF.B.7

NameDate

Figure — use these to answer the problems

Two different angles can give the same y-coordinate. That is why a restriction is needed.
(0.866, 0.500)
  • Angle30° = π/6 rad
  • x-coordinate0.866
  • y-coordinate0.500
  • cos 30°0.866
  • sin 30°0.500
Angle in degrees30
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Graphing Tangent”

    What is the period of y = tan(2x), in degrees?

    Answer

  2. From “Period and Phase Shift”

    y = cos(3x). What is the period, in degrees?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. sin θ = 0.5 and θ = 30°. What is the other solution below 360°?

    Answer

  2. Why must arcsin have a restricted range?

    • A function must give exactly one output.
    • Because that is the convention.

  3. cos θ = 1. What is θ in degrees?

    Answer

  4. cos θ = −1. What is θ in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. sin θ = 0 and θ is between 0 and 360, not 0. What is θ?

    Answer

  2. Why is arcsin restricted?

    • Otherwise one input would give many outputs.
    • It is easier to compute.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Angle

    sin θ = 1. What is θ, in degrees, between 0 and 360?

    Answerdegrees

  2. The Second One

    sin θ = 0.5 and θ = 30° is one answer. What is the other, between 0 and 360?

    Answerdegrees