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Cogito

Trigonometry · Chapter 4 · Lesson 2

Practice Worksheet

Solving Trigonometric Equations

The calculator gives one answer. The circle gives the rest.

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

NameDate

Figure — use these to answer the problems

Raise the wave and count how many times the curve reaches the same height in one cycle.
-8-8-6-6-4-4-2-222446688
y = 1 sin(1x) + 0
  • Point(1, 0.84)
a, amplitude1
b, cycles1
Point on the curve1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. sin θ = 0.866 gives 60°. 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 calculator rounds the others away.

  3. sin θ = 0.5. The larger solution below 360°, in degrees?

    Answer

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

    Answer

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

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. sin θ = −0.5. The quadrant IV solution, in degrees?

    Answer

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

    Answer

  3. sin θ = 2. How many solutions?

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

    Answer

  3. The Second Answer

    sin θ = 0.643 gives 40° on a calculator. What is the other solution below 360°, in degrees?

    Answerdegrees

  4. The Ferris Wheel

    A cabin height is h = 10 sin(30t) + 12 metres, t in minutes. At what value of 30t, in degrees, is the cabin first at 22 m?

    Answerdegrees