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Cogito

Integrated Math 3 · Chapter 6 · Lesson 3

Practice Worksheet

Solving Trigonometric Equations

The calculator gives one answer.

12 problems · about 22 minutes · F-TF.B.7

NameDate

Figure — use these to answer the problems

Draw a horizontal line across one cycle. It meets the curve twice, which is why there are two solutions.
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y = 1 sin(0x) + 0
  • Point(1, 0)
a, amplitude1
Point on the curve1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. sin θ = 0.643 gives 40°. The other solution below 360°, in degrees?

    Answer

  2. Why does a calculator return only one solution?

    • The inverse function has a restricted range, so it must pick one.
    • The others are rounded away.

  3. cos θ = 0.5, one answer is 60°. The other below 360°?

    Answer

  4. sin θ = −0.5, reference 30°. The quadrant III solution, in degrees?

    Answer

  5. Same equation. The quadrant IV solution?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin θ = 1. How many solutions between 0° and 360°?

    Answer

  2. sin θ = 2. How many solutions?

    Answer

  3. sin θ = 0.866 gives 60°. The other below 360°?

    Answer

Stretch Yourself

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

4 problems

  1. cos θ is negative. Which two quadrants hold the solutions?

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

  2. cos θ = 1. What is θ in degrees, below 360°?

    Answer

  3. The Other Answer

    sin θ = 0.5 gives 30°. What is the other solution below 360°, in degrees?

    Answerdegrees

  4. The Count

    sin θ = 0.5 with θ between 0° and 720°. How many solutions?

    Answer