# 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 expression , where .

Q3:

Find the solution set for given where .

• A,
• B,
• C,
• D,

Q4:

Find the value of which gives the minimum value of the expression , where .

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.

• A
• B1
• C
• D0

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.

Q20:

Find the value of without using a calculator, given .

• A
• B
• C
• D

Q21:

Find the solution set of given where .

• 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