Q1. Without using a calculator, give the exact trigonometric function value with rational denominator:

Background

Topic: Exact Trigonometric Values

This question tests your knowledge of special angles and their trigonometric values, specifically for .

Key Terms and Formulas:

• is a commonly memorized value from the unit circle.

• For , .

• Rationalizing the denominator may be required.

Step-by-Step Guidance

1. Recall the value of from the unit circle or special triangles.

2. Write the value in its simplest form.

3. If the denominator is irrational, rationalize it by multiplying numerator and denominator by .

Try solving on your own before revealing the answer!

Q2. Find the amount of each angle in the problem: Complementary angles with measures and .

Background

Topic: Complementary Angles

This question tests your understanding of complementary angles, which sum to .

Key Terms and Formulas:

• Complementary angles:

• Solve for .

Step-by-Step Guidance

1. Set up the equation: .

2. Combine like terms to get .

3. Solve for by dividing both sides by 3.

4. Find the measures of both angles: and .

Try solving on your own before revealing the answer!

Q3. Convert an angle in decimal degrees and round the second decimal place:

Background

Topic: Angle Conversion

This question tests your ability to convert degrees and minutes to decimal degrees.

Key Terms and Formulas:

• 1 degree = 60 minutes

• Decimal degrees = degrees + (minutes/60)

Step-by-Step Guidance

1. Write the angle as .

2. Convert the minutes to degrees: degrees.

3. Add this value to to get the decimal degree.

4. Round to the second decimal place.

Try solving on your own before revealing the answer!

Q4. Convert the angle to degrees, minutes, and seconds:

Background

Topic: Angle Conversion

This question tests your ability to convert decimal degrees to degrees, minutes, and seconds.

Key Terms and Formulas:

• 1 degree = 60 minutes

• 1 minute = 60 seconds

• To convert: Take the decimal part, multiply by 60 for minutes, then take the decimal part of minutes and multiply by 60 for seconds.

Step-by-Step Guidance

1. Separate the integer part: .

2. Multiply the decimal part () by 60 to get minutes.

3. Take the decimal part of the minutes and multiply by 60 to get seconds.

Try solving on your own before revealing the answer!

Q5. Find the value of

Background

Topic: Exact Trigonometric Values

This question tests your knowledge of special angles and their trigonometric values, specifically for .

Key Terms and Formulas:

• is a commonly memorized value from the unit circle.

• For , .

Step-by-Step Guidance

1. Recall the value of from the unit circle or special triangles.

2. Write the value in its simplest form.

Try solving on your own before revealing the answer!

Q6. The triangle is given. Find the missing angle or value of the variable.

Background

Topic: Triangle Angle Sum

This question tests your understanding of the sum of angles in a triangle and solving for unknowns.

Key Terms and Formulas:

• The sum of angles in a triangle is .

• If two angles are given, subtract their sum from to find the third angle.

Step-by-Step Guidance

1. Identify the given angles in the triangle.

2. Add the known angles together.

3. Subtract the sum from to find the missing angle.

Try solving on your own before revealing the answer!