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:

• Exact values for , , ,

Step-by-Step Guidance

1. Identify and .

2. Write the angle addition formula for sine: .

3. Recall the exact values: , , , .

4. Substitute these values into the formula, but do not simplify 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: 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:

• Exact value for

Step-by-Step Guidance

1. Recognize that , so .

2. Write the half-angle formula: .

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

4. Recall and substitute into the formula, but do not simplify yet.

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: Tangent Angle Addition Formula

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:

• Exact values for and

Step-by-Step Guidance

1. Identify and .

2. Write the tangent addition formula: .

3. Recall and .

4. Substitute these values into the formula, but do not simplify yet.

Try solving on your own before revealing the answer!

Q4. Find the exact value of using the fact that .

Background

Topic: Cosine Angle Addition Formula (Radians)

This question tests your ability to use the cosine addition formula with radian measures.

Key Terms and Formulas

• Cosine Addition Formula:

• Exact values for , , ,

Step-by-Step Guidance

1. Identify and .

2. Write the cosine addition formula: .

3. Recall the exact values: , , , .

4. Substitute these values into the formula, but do not simplify yet.

Try solving on your own before revealing the answer!

Q5. Find the exact value of using the fact that .

Background

Topic: Negative Angle and Half-Angle Formulas

This question tests your understanding of sine for negative angles and possibly the half-angle formula.

Key Terms and Formulas

• Odd Function Property:

• Sine Half-Angle Formula:

• Exact value for

Step-by-Step Guidance

1. Recognize that by the odd function property.

2. Express as a half-angle: .

3. Apply the sine half-angle formula: (since is in the first quadrant, sine is positive).

4. Recall and substitute into the formula, but do not simplify yet.

Try solving on your own before revealing the answer!