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Cogito

Integrated Math 3 · Chapter 5 · Lesson 1

Practice Worksheet

The Unit Circle and Radians

Trigonometry beyond the triangle.

12 problems · about 21 minutes · F-TF.A.1, F-TF.A.2

NameDate

Figure — use these to answer the problems

Drag past 90°, 180° and 270°, and watch which coordinate turns negative.
(-0.866, 0.500)
  • Angle150° = 5π/6 rad
  • x-coordinate-0.866
  • y-coordinate0.500
  • cos 150°-0.866
  • sin 150°0.500
Angle in degrees150
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is the reference angle for 200°, in degrees?

    Answer

  2. What decides the sign of a trigonometric value?

    • The quadrant, through the signs of the coordinates.
    • The size of the angle.

  3. What is sin 90°?

    Answer

  4. What is cos 180°?

    Answer

  5. Reference angle for 210°, in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin 210° as a decimal?

    Answer

  2. How many degrees is 2π radians?

    Answer

  3. Reference angle for 300°, in degrees?

    Answer

Stretch Yourself

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

4 problems

  1. In which quadrants is sine positive?

    • Quadrant I
    • Quadrant II
    • Quadrant III
    • Quadrant IV
    • Tick every box that applies.

  2. cos 300° as a decimal?

    Answer

  3. The Reference

    What is the reference angle for 150°, in degrees?

    Answerdegrees

  4. The Conversion

    How many degrees is π radians?

    Answerdegrees