In order to find its reference angle, we first need to find its corresponding angle between 0° and 360°. This is easy to do. We just keep subtracting 360 from it until it’s below 360. For instance, if our angle is 544°, we would subtract 360° from it to get 184° (544° – 360° = 184°).

What is reference angle and examples?

For example, to find the reference angle of -1000°, we will add 360° three times to it. It implies, – 1000° + 3(360°) = -1000° + 1080° = 80°. Therefore, 80° is the required reference angle of a negative angle of -1000°. If θ in a negative angle -θ is from 0 to 90 degrees, then its reference angle is θ.

What does find the reference angle mean?

The reference angle is the angle that the given angle makes with the x-axis. Regardless of where the angle ends (that is, regardless of the location of the terminal side of the angle), the reference angle measures the closest distance of that terminal side to the x-axis.

What is the reference angle of 180 degrees?

Reference angle for 180°: 0° Reference angle for 185°: 5°

What is the reference angle of 210?

The reference angle is found by calculating the difference between θ and the x-axis. In this problem, 210 is closest to 180, so 210∘−180∘=30∘ .

What is the reference angle of θ?

The reference angle for θ is 90∘ .

What is the reference angle of 45?

Since 45° is in the first quadrant, the reference angle is 45° .

What is the reference angle of 135?

135′ is in the second quadrant, so our reference angle is 180′-135 “, or 45′ .

What is the reference angle for 120?

Since the angle 120° is in the second quadrant, subtract 120° from 180° .

What is the reference angle of 150 degrees?

Looking at a graph, a 150° angle lies in quadrant II, therefore the reference angle is θ’ = 180° – 150° = 30°.

What is the measure of the reference angle for a 107 angle?

Trigonometry Examples

Since the angle 107° is in the second quadrant, subtract 107° from 180° .

What is the measure of the reference angle for an angle of negative 310 degrees in standard position?

Add 360° 360 ° to −310° – 310 ° . The resulting angle of 50° 50 ° is positive and coterminal with −310° – 310 ° . Since 50° is in the first quadrant, the reference angle is 50° .

What is the reference angle of 390?

Trigonometry Examples

Find an angle that is positive, less than 360° , and coterminal with 390° . Subtract 360° 360 ° from 390° 390 ° . The resulting angle of 30° 30 ° is positive, less than 360° 360 ° , and coterminal with 390° 390 ° .

What is the reference angle for 136 degrees?

Algebra Examples

Since the angle 136° is in the second quadrant, subtract 136° from 180° .

What is the reference angle for 65 degrees?

Since 65° is in the first quadrant, the reference angle is 65° .