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Cogito

Trigonometry · Chapter 2 · Lesson 2

Practice Worksheet

Reference Angles and the Four Quadrants

One acute angle can answer for all four.

12 problems · about 21 minutes · F-TF.A.2, F-TF.A.3

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 is sin 330° as a decimal?

    Answer

  3. Reference angle for 150°, in degrees?

    Answer

  4. Reference angle for 300°, in degrees?

    Answer

  5. Reference angle for 225°, in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin 150° as a decimal?

    Answer

  2. sin 210° as a decimal?

    Answer

  3. In which quadrants is tangent positive?

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

Stretch Yourself

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

4 problems

  1. Put these angles in order by size of reference angle, smallest first.

    Write 1 to 4 in the boxes to put these in order.

    • 170°
    • 200°
    • 310°
    • 225°

  2. cos 300° as a decimal?

    Answer

  3. The Reference

    What is the reference angle for 240°, in degrees?

    Answerdegrees

  4. The Sign

    In which quadrant are sine and cosine both negative?

    • Quadrant III.
    • Quadrant II.
    • Quadrant IV.