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Cogito

Trigonometry · Chapter 2 · Lesson 1

Practice Worksheet

The Unit Circle

The same ratios, freed from the triangle.

10 problems · about 21 minutes · F-TF.A.1, F-TF.A.2, F-TF.A.3

NameDate

Figure — use these to answer the problems

Push the angle past 90° and watch the coordinates go 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 Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Special Right Triangles”

    In a 30-60-90 triangle, the hypotenuse is 20. What is the short leg?

    Answer

  2. From “The Reciprocal Ratios”

    Which ratio is the reciprocal of cosine?

    • Secant.
    • Cosecant.

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. What is sin 270°?

    Answer

  2. On the unit circle, what is the cosine of an angle?

    • The x-coordinate of the terminal point.
    • The y-coordinate.

  3. What is cos 0°?

    Answer

  4. What is sin 0°?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. How many degrees is 2π radians?

    Answer

  2. What is cos 180°?

    Answer

Stretch Yourself

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

2 problems

  1. The Right Angle

    What is sin 90°?

    Answer

  2. The Radians

    How many degrees is π radians?

    Answerdegrees