# Worksheet: Solving a Trigonometric Equation

In this worksheet, we will practice solving a trigonometric equation using factoring or squaring.

Q1:

Find the set of values satisfying where . Give the answers to the nearest minute.

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Q2:

Find the set of values satisfying where . Give the answer to the nearest minute.

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Q3:

Find all the possible general solutions of .

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• E.

Q4:

Find the set of values satisfying where . Give the answers to the nearest second.

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Q5:

Find the set of values satisfying given .

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Q6:

Find the set of possible solutions of given .

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Q7:

Find the set of values satisfying where .

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Q8:

Find the set of values satisfying given .

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Q9:

Find all the possible general solutions of .

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• C.
• D.
• E.

Q10:

Find the set of values satisfying where . Give the answers to the nearest second.

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• E

Q11:

Find the set of values satisfying where . Give the answers to the nearest second.

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• E

Q12:

Find the set of values satisfying where . Give the answers to the nearest minute.

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Q13:

Consider the equation , where . Call this Equation A.

Create Equation B by squaring both sides of Equation A. Use the fact that to simplify Equation B.

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Now, use a double angle formula to further simplify Equation B.

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The solutions to Equation A are a subset of the solutions of Equation B. Using this, solve Equation A over the specified range.

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Q14:

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Q15:

If and , find the possible values of .

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Q16:

By first squaring both sides, or otherwise, solve the equation , where . Be careful to remove any extraneous solutions. Give your answers to two decimal places.

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Q17:

Find the set of values satisfying where . Give the answers to the nearest second.

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Q18:

If and , find the value of .

Q19:

Find the set of values satisfying where . Give the answer to the nearest minute.

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Q20:

If , then the general solution is , where .

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Q21:

If , then the number of solutions of the equation is .

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• B3
• C5
• D4

Q22:

The number of solutions of the equation is .

• A1
• B3
• Czero
• D2

Q23:

The solution set of the equation , where , is .

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