# Worksheet: Solving Trigonometric Equations Using Trigonometric Identities

In this worksheet, we will practice using Pythagorean trigonometric identities to solve trigonometric equations.

**Q1: **

Find the general solution of the equation .

- A or , where
- B or , where
- C or , where
- D or , where

**Q2: **

Find the value of which gives the maximum value of the equation where .

- A
- B
- C
- D

**Q4: **

Find the value of which gives the minimum value of the equation where .

- A
- B
- C
- D

**Q5: **

Find the measure of given where is a positive acute angle. Give the answer to the nearest minute.

- A
- B
- C
- D

**Q6: **

Find all possible solutions of that satisfy .

- A
- B
- C
- D

**Q7: **

Find the value of given where is a positive acute angle.

**Q8: **

Find the value of given where . Give the answer to the nearest second.

- A
- B
- C
- D

**Q9: **

Knowing that , find .

- A
- B
- C
- D
- E

**Q10: **

Find given where is a positive acute angle.

- A1
- B0
- C
- D

**Q11: **

Find the solution set of the equation given .

- A
- B
- C
- D

**Q12: **

Knowing that , find and .

- A
- B
- C
- D
- E

**Q13: **

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

**Q14: **

Consider the equation , where . We can solve this using the addition formula: .

If we compare to the right hand side of the addition formula we find that, for them to be equal, and that . Use these two equations to find the values of and , giving in radians.

- A ,
- B ,
- C ,
- D ,
- E ,

Using your values for and , solve the equation to find the solutions for the original equation.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q15: **

Find in degrees given where is a positive acute angle.

**Q16: **

Find the set of values satisfying where .

- A
- B
- C
- D

**Q17: **

Determine the value of to the nearest second, given that , where is acute.

- A
- B
- C
- D

**Q18: **

Find the solution set of given where .

- A
- B
- C
- D

**Q19: **

Find the value of given where is an acute angle.

- A
- B
- C
- D

**Q20: **

Find the value of without using a calculator, given .

- A
- B
- C
- D

**Q22: **

Find the value of that gives the minimum value of given where .

**Q23: **

Find the value of that gives the maximum value of given where .

**Q24: **

Find the set of solutions for given , where .

- A
- B
- C
- D

**Q25: **

Find the set of values satisfying where .

- A
- B
- C
- D