# Worksheet: Solving Trigonometric Equations with the Double-Angle Identity

In this worksheet, we will practice solving trigonometric equations using the double-angle identity.

Q1:

If , find the solution set of .

• A
• B
• C
• D

Q2:

Find in degrees given where is a positive acute angle.

Q3:

Find the general solution to the equation .

• A , , where
• B , , where
• C , , where
• D , , where
• E , , where

Q4:

Find the set of possible solutions of given .

• A
• B
• C
• D

Q5:

Find the solution set for given where .

• A
• B
• C
• D

Q6:

Find all the possible solutions, that is, the general solution, of the equation .

• A (where )
• B , (where )
• C , (where )
• D , (where )
• E , (where )

Q7:

If , find the solution set of .

• A
• B
• C
• D

Q8:

Find the solution set for given where .

• A
• B
• C
• D

Q9:

Solve , where .

• A
• B
• C
• D
• E

Q10:

By using the half angle formula , or otherwise, solve the equation , where .

• A
• B
• C
• D
• E

Q11:

Find the solution set for given where .

• A
• B
• C
• D

Q12:

Find all the possible general solutions of .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q13:

Find the set of values satisfying , where .

• A
• B
• C
• D
• E

Q14:

Find the value of given where is an acute angle. Give the answer to the nearest degree.

Q15:

Find the value of without using a calculator, given .

• A
• B
• C
• D12

Q16:

Find the general solution to the equation .

• A , , where
• B , , where
• C , , where
• D , , where
• E , , where

Q17:

Find the value of given where is an acute angle. Give the answer to the nearest minute.

• A
• B
• C
• D

Q18:

Find the value of in degrees given where is an acute angle.

Q19:

Find the value of given giving the answer to the nearest second.

• A or
• B or
• C or
• D or

Q20:

Find the set of possible values of which satisfy where .

• A
• B
• C
• D

Q21:

Find given where is a positive acute angle.

Q22:

Find the set of solutions for given where .

• A
• B
• C
• D

Q23:

Find the set of solutions in the range for the equation .

• A
• B
• C
• D
• E