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Cogito

AP Precalculus · Chapter 6 · Lesson 3

Practice Worksheet

Inverse Trigonometric Functions

Going back from a ratio to an angle.

12 problems · about 22 minutes · AP Precalculus 3.11, 3.12

NameDate

Figure — use these to answer the problems

Draw a horizontal line across one cycle. It meets the curve twice, which is why an equation has two solutions per turn.
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y = 1 sin(0x) + 0
  • Point(1, 0)
a, amplitude1
Point on the curve1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. sin θ = 0.5 gives 30°. What is the other solution below 360°, in degrees?

    Answer

  2. Why does a calculator return only one solution?

    • The inverse has a restricted range, so it must pick one.
    • The others are rounded away.

  3. sin θ = 1. What is θ in degrees?

    Answer

  4. cos θ = 1. What is θ in degrees?

    Answer

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

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin θ = 0.866 gives 60°. The other solution below 360°?

    Answer

  2. sin θ = 2. How many solutions?

    Answer

  3. sin θ = 0.5 with θ between 0° and 720°. How many solutions?

    Answer

Stretch Yourself

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

4 problems

  1. Match each inverse function with its range.

    Draw a line from each item on the left to its match on the right.

    • arcsin
    • arccos
    • arctan
    • Negative 90 to 90 degrees, ends included
    • Zero to 180 degrees
    • Negative 90 to 90 degrees, ends excluded

  2. sin θ = 0.643 gives 40°. The other solution below 360°?

    Answer

  3. The Second Solution

    sin θ = 0.5 gives 30°. What is the other solution below 360°, in degrees?

    Answerdegrees

  4. The Range

    How many degrees does the range of arccos span?

    Answer