What Is The Reference Angle For? The reference angle is used for the purpose of the simplification of the calculations in the trigonometric function value at different angles. It is noted that, even for the larger angles, the reference angle should be less than 90 degrees.

What is the reference angle of negative 30? Since 330 is thirty less than 360, and since 360° = 0°, then the angle 330° is thirty degrees below (that is, short of) the positive x-axis, in the fourth quadrant. So its reference angle is 30°.

What is the reference angle of degree angle? When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.

What is the reference angle of 45? Trigonometry Examples Since 45° is in the first quadrant, the reference angle is 45° .

## What is the reference angle of 270 degrees?

Reference angle for 270°: 90° (π / 2)

## What is the reference angle of 235?

The reference angle for 235 is 55 degrees. If the terminal side of the angle is in the fourth quadrant, we take the angle and subtract it from 360 degrees.

## What is the reference angle for 570?

Subtract 360° 360 ° from 570° 570 ° . The resulting angle of 210° 210 ° is positive, less than 360° 360 ° , and coterminal with 570° 570 ° .

## What is reference angle and examples?

For example, 23∘ is in quadrant I, and its reference angle is 23∘ . Or, 157∘ is in quadrant II, and its reference angle is 180∘−157∘=23∘ 180 ∘ − 157 ∘ = 23 ∘ . Negative angles (strictly between 0∘ and −180∘ ) put you in quadrants III and IV. For example, −23∘ is in quadrant IV, and its reference angle is 23∘ .

## What is the reference angle of 495?

The coterminal angle is 495° − 360° = 135°. Therefore, the reference angle of 495° is 45°.

## What is the reference angle of 240?

A 240-degree angle is between 180 and 270 degrees, so its terminal side is in QIII. Do the operation indicated for that quadrant. Subtract 180 from 240. You find that 240 – 180 = 60, so the reference angle is 60 degrees.

## What is the reference angle for 135?

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

## What is the reference angle of 150?

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

## What is the reference angle of 90 degrees?

Since 90° is in the first quadrant, the reference angle is 90° .

## What is the Coterminal angle of 40?

Illustration showing coterminal angles of 40° and -320°. Coterminal angles are angles drawn in standard position that have a common terminal side.

## What is the reference angle of 22π 3?

Subtract 2π 2 π from 22π3 22 π 3 . The resulting angle of 16π3 16 π 3 is positive, less than 2π 2 π , and coterminal with 22π3 22 π 3 . Subtract 2π 2 π from 16π3 16 π 3 . The resulting angle of 10π3 10 π 3 is positive, less than 2π 2 π , and coterminal with 22π3 22 π 3 .

## What is the reference angle of 520?

Find an angle that is positive, less than 360° , and coterminal with 520° . Subtract 360° 360 ° from 520° 520 ° . The resulting angle of 160° 160 ° is positive, less than 360° 360 ° , and coterminal with 520° 520 ° .

## What is the reference angle for 370?

Trigonometry Examples Add 360° 360 ° to −370° – 370 ° . The resulting angle of −10° – 10 ° is coterminal with −370° – 370 ° but isn’t positive. Repeat the step.

## How do I know if I have SOH CAH TOA?

SOH: Sin(θ) = Opposite / Hypotenuse. CAH: Cos(θ) = Adjacent / Hypotenuse. TOA: Tan(θ) = Opposite / Adjacent.

## Why are angles 135 and 495 Coterminal angles?

Trigonometry Examples Subtract 360° 360 ° from 495° 495 ° . The resulting angle of 135° 135 ° is positive, less than 360° 360 ° , and coterminal with 495° 495 ° .

## What is the Coterminal angle of 120?

For example, angles measuring 120° and – 240° are coterminal.

## Can a reference angle be negative?

The reference angle of an angle is always non-negative i.e., a negative reference angle doesn’t exist. The reference angle of any angle always lies between 0 and π/2 (both inclusive).

## What is the reference angle of 720?

Subtract 360° 360 ° from 720° 720 ° . The resulting angle of 360° 360 ° is positive, less than 360° 360 ° , and coterminal with 720° 720 ° .

## What is the reference angle for a 390 angle?

Since 30° is in the first quadrant, the reference angle is 30° .