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

**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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**Q4: **

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

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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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**Q10: **

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

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**Q11: **

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

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**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: **

Solve , where . Give your answer in radians to three significant figures.

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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 .