# Worksheet: Solving a Trigonometric Equation by Squaring

Q1:

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
• C
• 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
• C
• D
• E

Q2:

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

• A
• B
• C
• D
• E

Q3:

If and , find the possible values of .

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

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
• C
• D
• E

Q5:

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

• A
• B
• C
• D
• E

Q6:

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

• A
• B
• C
• D
• E

Q7:

If and , find the value of .

• A
• B
• C
• D
• E