Math III - 7.3 DHQ (2nd) 12/5

Front

What is the reference angle?

Back

The reference angle is the acute angle formed by the terminal side of a given angle and the x-axis. It is always positive and is measured in the range of 0° to 90°.

Front

How do you find the reference angle for an angle in the second quadrant?

Back

To find the reference angle for an angle in the second quadrant, subtract the angle from 180°. For example, for an angle of 163°, the reference angle is 180° - 163° = 17°.

Front

How do you find the reference angle for an angle in the first quadrant?

Back

The reference angle for an angle in the first quadrant is the angle itself. For example, for an angle of 73°, the reference angle is 73°.

Front

How do you find the reference angle for an angle in the third quadrant?

Back

To find the reference angle for an angle in the third quadrant, subtract 180° from the angle. For example, for an angle of 207°, the reference angle is 207° - 180° = 27°.

Front

How do you find the reference angle for an angle in the fourth quadrant?

Back

To find the reference angle for an angle in the fourth quadrant, subtract the angle from 360°. For example, for an angle of 307°, the reference angle is 360° - 307° = 53°.

Front

What is the reference angle for -43°?

Back

To find the reference angle for a negative angle, first convert it to a positive angle by adding 360°. For -43°, the positive angle is 360° - 43° = 317°. The reference angle is 360° - 317° = 43°.

Front

What is the reference angle for 47°?

Back

The reference angle for 47° is simply 47° since it is in the first quadrant.

Front

What is the significance of the reference angle in trigonometry?

Back

The reference angle is significant because it allows us to find the values of trigonometric functions for angles greater than 90° by relating them to their corresponding acute angles.

Front

How do you determine the quadrant of an angle?

Back

The quadrant of an angle can be determined by its degree measure: 0° to 90° (1st quadrant), 90° to 180° (2nd quadrant), 180° to 270° (3rd quadrant), and 270° to 360° (4th quadrant).

Front

What is the reference angle for 107°?

Back

To find the reference angle for 107°, subtract it from 180°. The reference angle is 180° - 107° = 73°.