Solving Trigonometric Equations: Practice Exercises

Here are various Exercises to accompany the section Solving Trigonometric Equations.  

Inverse Trigonometric Functions

  1. Use the formulas from the text for sin-1, cos-1, and tan-1 to write formulas for all solutions to the following equations.  Note: If you recognize exact values using the table in the text, you may give exact values for these inverse trigonometric functions.  Otherwise, you should simply use your calculator to give approximate values.
    1. - = sin(x)
    2. 0.7 = sin(x)
    3. -2 = cos(x)
    4. 1 = tan(x)
    5. - = tan(x)
    6. 0.6 = cos(x)

    Solution.

Solving Trigonometric Equations

  1. Use the formulas from the text for sin-1, cos-1, and tan-1 to write formulas for all solutions to the following equations.  Note: If you recognize exact values using the table in the text, you may give exact values for these inverse trigonometric functions.  Otherwise, you should simply use your calculator to give approximate values.
    1. 4 = -5sin(x) + 1
    2. 4 = -5sin(1 - 2x) + 1
    3. -7 = 2cos(x) - 3
    4. 5 = 3tan(x) + 2
    5. 5 = 3tan(-4x + p/3) + 2
    6. 1 = -5cos(3x - p/5) + 4

    Solution.

  2. Give the specific solution(s) requested to each of the following equations.
    1. The first solution of 4 = -5sin(1 - 2x) + 1 that is less than -6.
    2. The first solution of 5 = 3tan(-4x + p/3) + 2 that is greater than 4.
    3. The solutions of 1 = -5cos(3x - p/5) + 4 that are between p/2 and p.

    Solution.

Go to Geometry and Trigonometric Functions .

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