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

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

**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 )

**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

**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