07.2 - Unit Circle

For θ = 160°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant II, 20°

• Quadrant III, 70°

• Quadrant I, 160°

• Quadrant IV, 20°

Answer explanation

For θ = 160°, the angle is in Quadrant II since it is between 90° and 180°. The reference angle θ' is found by subtracting 160° from 180°, giving us 20°. Thus, the correct answer is Quadrant II, 20°.

For θ = 200°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant III, 20°

• Quadrant II, 20°

• Quadrant III, 160°

• Quadrant IV, 20°

Answer explanation

For θ = 200°, the angle is in Quadrant III (180° to 270°). The reference angle θ' is found by subtracting 180° from 200°, giving us 20°. Thus, the correct answer is Quadrant III, 20°.

For θ = 310°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant IV, 50°

• Quadrant III, 40°

• Quadrant II, 70°

• Quadrant I, 50°

Answer explanation

For θ = 310°, the angle is in Quadrant IV since it is between 270° and 360°. The reference angle θ' is calculated as 360° - 310° = 50°. Thus, the correct answer is Quadrant IV, 50°.

For θ = 230°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant III, 50°

• Quadrant II, 40°

• Quadrant IV, 50°

• Quadrant III, 40°

Answer explanation

For θ = 230°, the angle is in Quadrant III (180° to 270°). The reference angle θ' is found by subtracting 180° from 230°, giving us 50°. Thus, the correct answer is Quadrant III, 50°.

For θ = 100°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant II, θ' = 80°

• Quadrant I, θ' = 100°

• Quadrant III, θ' = 10°

• Quadrant IV, θ' = 100°

Answer explanation

For θ = 100°, the angle is in Quadrant II because it is between 90° and 180°. The reference angle θ' is found by subtracting θ from 180°, giving θ' = 180° - 100° = 80°.

For θ = 440°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant IV, Reference angle θ' = 60°

• Quadrant II, Reference angle θ' = 40°

• Quadrant I, Reference angle θ' = 80°

• Quadrant III, Reference angle θ' = 100°

Answer explanation

To find the quadrant for θ = 440°, subtract 360° to get 80°, which is in Quadrant I. The reference angle θ' is the acute angle from the x-axis, so θ' = 80°. Thus, the correct answer is Quadrant I, Reference angle θ' = 80°.

For θ = 500°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant IV, Reference angle = 30°

• Quadrant III, Reference angle = 70°

• Quadrant I, Reference angle = 50°

• Quadrant II, Reference angle = 40°

Answer explanation

To find the quadrant for θ = 500°, subtract 360° to get 140°, which is in Quadrant II. The reference angle is 180° - 140° = 40°. Thus, the correct answer is Quadrant II, Reference angle = 40°.

For θ = 705°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant I, θ' = 45°

• Quadrant II, θ' = 75°

• Quadrant III, θ' = 15°

• Quadrant IV, θ' = 15°

Answer explanation

To find the quadrant for θ = 705°, subtract 360°: 705° - 360° = 345°. This angle is in Quadrant IV. The reference angle θ' is 360° - 345° = 15°. Thus, the correct answer is Quadrant IV, θ' = 15°.

For θ = 385°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant I, θ' = 25°

• Quadrant II, θ' = 5°

• Quadrant III, θ' = 35°

• Quadrant IV, θ' = 15°

Answer explanation

To find the quadrant for θ = 385°, subtract 360° to get 25°, which is in Quadrant I. The reference angle θ' is 25°, confirming the correct choice: Quadrant I, θ' = 25°.

For θ = 610°, in which quadrant does the terminating ray reside and what is the reference angle θ'?

• Quadrant II, 70°

• Quadrant IV, 70°

• Quadrant I, 250°

• Quadrant III, 70°

Answer explanation

To find the quadrant for θ = 610°, subtract 360° to get 250°, which is in Quadrant III. The reference angle θ' is 610° - 360° = 250° - 180° = 70°. Thus, the correct answer is Quadrant III, 70°.