Asked by: Modesto Siman
science space and astronomy

What is the reference angle?

Last Updated: 9th March, 2020

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The reference angle is the positive acute angle that can represent an angle of any measure. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

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Likewise, what is reference angle and examples?

Finding Reference Angles Example 1: Find the reference angle for 150 degrees. 180 - 150 = 30 degrees. The reference angle is 30 degrees. If the terminal side of the angle is in the 3rd quadrant, we take 180 degrees and subtract it from the angle measure. 360 - 300 = 60 degrees.

Additionally, what is the reference angle of 210? 210 degrees is 30 degrees past 180, which means the reference angle is 30 degrees. Example: If we were asked to calculate the reference angle for 330 degrees, we would first sketch it. Next, we would see that it is 30 degrees from 360 degrees, which is the smallest angle to the x-axis and therefore the reference angle.

Also to know is, what is the reference angle of 90 degrees?

Reference angle for 90°: 90° (π / 2)

Can reference angles be negative?

It is always positive Regardless of which quadrant we are in, the reference angle is always made positive. Drag the point clockwise to make negative angles, and note how the reference angle remains positive.

Related Question Answers

Maryana Wane

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What is the reference angle for 225?

Add 360° 360 ° to −225° - 225 ° . The resulting angle of 135° 135 ° is positive and coterminal with −225° - 225 ° . Since the angle 135° is in the second quadrant, subtract 135° from 180° .

Zak Arambarri

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What is a Quadrantal angle?

A Quadrantal Angle is an angle in standard position with terminal side on the x-axis or y-axis. Some examples are the angles located at 0°, 90°, 180°, 270°, 360°, 450°, as well as -90°, -180°, -270°, -360°

Shan Pichard

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Is reference angle always positive?

Reference Angles. A reference angle for a given angle in standard position is the positive acute angle formed by the $x$-axis and the terminal side of the given angle. Reference angles, by definition, always have a measure between 0 and .

Malinda Ubiedo

Explainer

What are reference angles used for?

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.

Anda Schweisfurth

Pundit

What is the reference angle of 120 degrees?

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

Abdelhalak Dubrau

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What is the reference angle for 315 degrees?

Trigonometry Examples
Add 360° 360 ° to −315° - 315 ° . The resulting angle of 45° 45 ° is positive and coterminal with −315° - 315 ° . Since 45° is in the first quadrant, the reference angle is 45° .

Cristinela Arcila

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What type of angle is 315 degrees?

The larger measure (315°) is called the reflex angle RPQ.

Emran Orengo

Pundit

What is basic angle in trigonometry?

Angle (Trigonometry) Definition: An angle which has its vertex at the origin, and one side lying on the positive x-axis. It can have a measure which positive or negative and can be greater than 360°. In trigonometry, an angle is drawn in what is called the "standard position".

Roswitha Lawa

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What's a Coterminal angle?

Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians. There are an infinite number of coterminal angles that can be found.

Alexa Djumaev

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How do I find the length of an arc?

To find arc length, start by dividing the arc's central angle in degrees by 360. Then, multiply that number by the radius of the circle. Finally, multiply that number by 2 × pi to find the arc length.

Dreama Sanches

Teacher

What is a reference angle in the unit circle?

A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis. Explain how the sine of an angle in the second quadrant differs from the sine of its reference angle in the unit circle. The sine values are equal.

Hedwig Garrastacho

Teacher

What is the reference angle of pi?

The reference angle is always between 0 and 2π radians (or between 0 and 90 degrees).

Quintiliano Heidepeter

Reviewer

How do you find the reference angle for 1406?

Answer Expert Verified
That leaves you with 1406-1080 degrees unaccounted for, which is 326 degrees. Head around the origin again in the counterclockwise direction 326 degrees, which is 360-326 degrees short of a full rotation (34 degrees). So the reference angle is either -34 degrees or 326 degrees.

Doroteo Rong

Reviewer

What is the reference angle for 5 radians?

Reference angle is the smallest angle between the terminal side of the angle and the x-axis. Accordingly, the reference angle for 5 would be angle 5 it self. Angle -5 is the angle 355. Hence the reference angle for -5 would also be360-355= 5.

Claro Ferven├ža

Reviewer

What is the reference angle for 15 in standard position?

Since 15° is in the first quadrant, the reference angle is 15° .

Marius Codrea

Supporter

What is the reference angle Whenta 5pi 6?

Answer Expert Verified
The reference angle is the smallest angle that the terminal side of the angle makes with the x-axis. Given that here π/2 < Ф < π, the angle is in the second quadrant. tangent negative. Furthermore, the reference angle is π - Ф = π - 5π/6 = π/6.

Eleodoro Mesia

Supporter

How do you find the reference angle of an angle greater than 360?

The rule is that if the angle is greater than 360 degrees, subtract 360 in succession until the angle is smaller than 360 degrees. In our scenario 545 - 360 = 185. Next, locate the angle in either quadrant I, II, III or IV. Use the following rules to determine the reference angle, given the quadrant.