# What is a reference angle unit circle?

Space and AstronomyFor each angle drawn in standard position, there is a related angle known as a reference angle. This is **the angle formed by the terminal side and the x-axis**. The reference angle is always considered to be positive, and has a value anywhere from 0° to 90°. Two angles are shown below in standard position.

Contents:

## How do you find the reference angle on a unit circle?

Video quote: *And we're going to subtract 180 from it to find the reference angle. So this one's just going to be 60 degrees. So it's the given angle minus 180.*

## What is reference angle?

When an angle is drawn on the coordinate plane with a vertex at the origin, the reference angle is **the angle between the terminal side of the angle and the x-axis**. The reference angle is always between 0 and 2π radians (or between 0 and 90 degrees).

## How do you find the reference angle?

So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°. **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 reference angle on the unit?

What is a reference angle. Reference Angle: **the acute angle between the terminal arm/terminal side and the x-axis**. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis.

## How many reference angles are there in the unit circle?

Look at the degrees unit circle, and you will see that the reference angles are **0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, and 330 degrees**. The equivalent angles in radians are 0, pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi, 7pi/6, 5pi/4, 4pi/3, 3pi/2, 5pi/3, 7pi/4, and 11pi/6.

## 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 is the reference angle of 235?

55 degrees

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 of 120?

60°

Reference angle for 120°: **60°** (π / 3)

## What is the reference angle of 210?

210 degrees is **30 degrees** past 180, which means the reference angle is 30 degrees.

## What is the reference angle of 320?

40°

Trigonometry Examples

Add 360° 360 ° to −320° – 320 ° . The resulting angle of 40° **40 °** is positive and coterminal with −320° – 320 ° . Since 40° is in the first quadrant, the reference angle is 40° .

## What is the reference angle for 290?

Since the angle 290° is in the fourth quadrant, **subtract 290° from 360°** .

## What is the reference angle of 315?

45∘

So, the reference angle is 360∘−315∘=**45∘** . ∴ We have found the reference angle for 315 degrees as 45∘ .

## What is the reference angle of 330?

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 150?

30°

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 215?

Add 360° 360 ° to −215° – 215 ° . The resulting angle of **145°** 145 ° is positive and coterminal with −215° – 215 ° .

## What is the reference angle of 345?

The reference angle of 345 is 360 – 345. That is **15°**.

## What is the reference angle of 225 degrees?

Trigonometry Examples

Since the angle **180°** is in the third quadrant, subtract 180° from 225° .

## What is the Coterminal angle of 216?

Trigonometry Examples

The resulting angle of **144°** 144 ° is positive and coterminal with −216° – 216 ° . Since the angle 144° is in the second quadrant, subtract 144° from 180° .

## What is the reference angle for 275?

Since the angle 275° is in the fourth quadrant, **subtract 275° from 360°** .

## What is the reference angle of 410?

Subtract 360° 360 ° from 410° 410 ° . The resulting angle of **50° 50 °** is positive, less than 360° 360 ° , and coterminal with 410° 410 ° .

## What is the reference angle of 1230?

Trigonometry Examples

Subtract 360° 360 ° from 1230° 1230 ° . The resulting angle of **870° 870 °** is positive and coterminal with 1230° 1230 ° but isn’t less than 360° 360 ° .

## What is the reference angle of 540?

Subtract 360° 360 ° from 540° 540 ° . The resulting angle of **180° 180 °** is positive, less than 360° 360 ° , and coterminal with 540° 540 ° .

## What is the reference angle for 400?

40°

Trigonometry Examples

Since **40°** is in the first quadrant, the reference angle is 40° .

## What is the reference angle of 80?

80°

Trigonometry Examples

Since **80°** is in the first quadrant, the reference angle is 80° .

## 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 85?

Trigonometry Examples

Since **85°** is in the first quadrant, the reference angle is 85° .

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