Trigonometry Quiz

If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies. -3π/4

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

The angle -3π/4 is equivalent to 5π/4 when converted to a positive angle. This angle lies in Quadrant III, where both sine and cosine values are negative.

If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies. 620°

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

To find the quadrant for 620°, first reduce it by subtracting 360°: 620° - 360° = 260°. The angle 260° lies between 180° and 270°, which places it in Quadrant IV.

If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies. -135°

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

An angle of -135° is equivalent to 225° when converted to a positive angle (360° - 135°). The terminal side of 225° lies in Quadrant III, but since we are considering -135°, it actually lies in Quadrant II.

If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies. 4.7π/4

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

To find the quadrant for 4.7π/4, first convert it to degrees: 4.7π/4 = 4.7 * 45 = 211.5°. Since 180° < 211.5° < 270°, the angle lies in Quadrant III.

If each angle has the given measure and is in standard position, determine the quadrant in which its terminal side lies. -330°

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

To find the quadrant for -330°, add 360° to get 30°. The angle 30° is in Quadrant I, where both x and y coordinates are positive. Thus, the terminal side of -330° lies in Quadrant I.

Change each degree measure to radian measure in terms of π. 90°

• π/2

• π/3

• 2π/3

• π/4

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For 90°, it becomes 90 × (π/180) = π/2. Thus, the correct answer is π/2.

Change each degree measure to radian measure in terms of π. 220°

• 11π/9

• 5π/6

• 7π/6

• 4π/3

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For 220°, it becomes 220 × (π/180) = 11π/9. Thus, the correct answer is 11π/9.

Change each degree measure to radian measure in terms of π. 15°

• π/12

• π/9

• π/6

• π/18

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For 15°, it becomes 15 × (π/180) = π/12. Thus, the correct answer is π/12.

Change each radian measure to degree measure. 5π/9

• 100°

• 90°

• 80°

• 70°

Answer explanation

To convert radians to degrees, multiply by 180/π. For 5π/9, the calculation is (5π/9) * (180/π) = 100°. Thus, the correct answer is 100°.

Change each radian measure to degree measure. -π/6

• -30°

• -45°

• -60°

• -90°

Answer explanation

To convert -π/6 radians to degrees, use the formula: degrees = radians × (180/π). Thus, -π/6 × (180/π) = -30°. Therefore, the correct answer is -30°.