Q1. Give two positive and two negative angles that are coterminal with the given quadrantal angle.

Background

Topic: Coterminal Angles

This question tests your understanding of coterminal angles, which are angles that share the same terminal side when drawn in standard position. You need to find both positive and negative angles that are coterminal with a given angle (e.g., 90°, 180°, 0°, 270°).

Key Terms and Formulas:

• Coterminal Angles: Angles that differ by integer multiples of 360°.

• Formula: , where is any integer.

Step-by-Step Guidance

1. Start with the given angle (e.g., 90°).

2. To find positive coterminal angles, add 360° one or more times: , , etc.

3. To find negative coterminal angles, subtract 360° one or more times: , , etc.

4. Repeat this process for each given angle (180°, 0°, 270°).

Try solving on your own before revealing the answer!

Q2. Write an expression that generates all angles coterminal with each angle. Let n represent any integer.

Background

Topic: General Expression for Coterminal Angles

This question asks you to write a general formula for all angles coterminal with a given angle, using an integer variable (n) to represent all possible multiples of 360°.

Key Terms and Formulas:

• Coterminal Angles: Angles that differ by integer multiples of 360°.

• General Expression: , where is any integer.

Step-by-Step Guidance

1. Identify the given angle (e.g., 30°, 45°, 135°, etc.).

2. Write the expression for each angle, replacing with the specific angle value.

3. Explain that can be any integer, so this formula generates all possible coterminal angles (both positive and negative).

4. Apply this formula to each angle listed in the question.

Try solving on your own before revealing the answer!