Q1. Find the exact value of sin(105°) using the fact that 105° = 60° + 45°.

Background

Topic: Trigonometric Angle Addition Formulas

This question tests your ability to use the sine addition formula to find the exact value of a sine function for a non-standard angle.

Key Terms and Formulas

• Angle Addition Formula for Sine:

• Reference angles: 60° and 45°

• Exact values: , , ,

Step-by-Step Guidance

1. Recognize that , so you can use the sine addition formula.

2. Write the formula: .

3. Substitute the exact values for , , , and into the formula.

4. Set up the expression for simplification, but do not combine the terms yet.

Try solving on your own before revealing the answer!

Q2. Find the exact value of cos(67.5°) using the fact that .

Background

Topic: Trigonometric Half-Angle Formulas

This question tests your ability to use the cosine half-angle formula to find the exact value for a non-standard angle.

Key Terms and Formulas

• Cosine Half-Angle Formula:

• Reference angle:

• Exact value:

Step-by-Step Guidance

1. Recognize that , so you can use the half-angle formula for cosine.

2. Write the formula: .

3. Determine the sign: Since is in the first quadrant, cosine is positive.

4. Substitute into the formula and set up the expression for simplification.

Try solving on your own before revealing the answer!

Q3. Find the exact value of tan(195°) using the fact that 195° = 45° + 150°.

Background

Topic: Trigonometric Angle Addition Formulas

This question tests your ability to use the tangent addition formula to find the exact value for a non-standard angle.

Key Terms and Formulas

• Tangent Addition Formula:

• Reference angles: and

• Exact values: ,

Step-by-Step Guidance

1. Recognize that , so you can use the tangent addition formula.

2. Write the formula: .

3. Substitute the exact values for and into the formula.

4. Set up the expression for simplification, but do not combine the terms yet.

Try solving on your own before revealing the answer!