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Cogito

Trigonometry · Chapter 4 · Lesson 3

Practice Worksheet

Composing Functions and Inverses

Sometimes the two cancel, and sometimes they do not.

12 problems · about 22 minutes · F-TF.B.6, F-BF.B.4

NameDate

Figure — use these to answer the problems

Build the triangle a composition describes, then read the other ratio straight off it.
adjacent = 4opposite = 3hyp = 536.87°
  • sin — opposite over hypotenuse0.60
  • cos — adjacent over hypotenuse0.80
  • tan — opposite over adjacent0.75
  • The marked angle36.87°
Adjacent leg4
Opposite leg3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is arcsin(sin 170°), in degrees?

    Answer

  2. Which composition always returns the original input?

    • sin(arcsin x), for x between −1 and 1.
    • arcsin(sin θ), for every θ.

  3. cos(arccos 0.4)?

    Answer

  4. arcsin(sin 40°), in degrees?

    Answer

  5. arcsin(sin 200°), in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. cos(arcsin 0.8)?

    Answer

  2. sin(arccos 0)?

    Answer

  3. tan(arctan 5)?

    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
    • −90° to 90°, endpoints included
    • 0° to 180°
    • −90° to 90°, endpoints excluded

  2. arccos(cos 300°), in degrees?

    Answer

  3. The Cancel

    What is sin(arcsin 0.3)?

    Answer

  4. The Surprise

    What is arcsin(sin 150°), in degrees?

    Answerdegrees