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Cogito

AP Precalculus · Chapter 6 · Lesson 1

Practice Worksheet

The Unit Circle and Radians

Freeing the ratios from the triangle.

12 problems · about 21 minutes · AP Precalculus 3.3, 3.4

NameDate

Figure — use these to answer the problems

Drag past 90°, 180° and 270°, and watch which coordinate turns negative.
(0.500, 0.866)
  • Angle60° = π/3 rad
  • x-coordinate0.500
  • y-coordinate0.866
  • cos 60°0.500
  • sin 60°0.866
Angle in degrees60
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is sin 180°?

    Answer

  2. Why does calculus use radians rather than degrees?

    • Arc length and the calculus formulas come out clean, with no conversion factor.
    • Because radians are smaller numbers.

  3. What is sin 90°?

    Answer

  4. What is cos 180°?

    Answer

  5. What is sin 0°?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many degrees is 2π radians?

    Answer

  2. How many degrees is π ÷ 2 radians?

    Answer

  3. Radius 5, angle 3 radians. Arc length?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each quantity by which coordinate it reads.

    Write each item under the heading it belongs to: Cosine · Horizontal position on the circle · Sine · Vertical position on the circle

    The x-coordinate

    The y-coordinate

  2. What is cos 90°?

    Answer

  3. The Conversion

    How many degrees is π radians?

    Answerdegrees

  4. The Coordinate

    On the unit circle, what is cos 0°?

    Answer