Worksheet: Solving a Trigonometric Equation by Squaring

In this worksheet, we will practice solving trigonometric equations by squaring both sides.

Q1:

If and , find the possible values of .

• A ,
• B ,
• C ,
• D ,
• E ,

Q2:

If and , find the value of .

Q3:

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

• A
• B
• C
• D
• E

Q4:

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.

• A
• B
• C
• D
• E

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

• A
• B
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• D
• E

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

• A
• B
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• D
• E

Q5:

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.

• A
• B
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• D
• E

Q6:

• A
• B
• C
• D
• E

Q7:

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

• A
• B
• C
• D
• E