Are Coterminal angles and reference angles the same?

Asked By: Shirlee Naftulin | Last Updated: 19th January, 2020
Category: science space and astronomy
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If two angles in standard position have the same terminal side, they are called coterminal angles. The reference angle is the acute angle (the smallest angle) formed by the terminal side of the given angle and the x-axis.

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In respect to this, how do you find the 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.

One may also ask, do Quadrantal angles have reference angles? Quadrantal Angles: Angles 0°, 90°, 180°, 270°, and 360° do not have reference angles because they are quadrantal angles.

Additionally, what are reference angles?

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.

What is the Coterminal angle of 60?

Therefore, 60 degrees and -300 degrees are coterminal angles. The -300 degree rotation is pictured here. Infinitely many other angles are coterminal to 60 degrees. Each time you add or subtract a multiple of 360 degrees to 60 degrees, you will end up with a coterminal angle of 60 degrees.

39 Related Question Answers Found

What is the Coterminal angle of 45?

Coterminal Angles are angles in standard position that have the same Initial Side and the same Terminal side. For example 45°, 405° and -315° are coterminal angles because all three angles have the same initial side (the x axis) and they share a same terminal side.

Why do reference angles work?

Reference Angles. The use of reference angles is a way to simplify the calculation of the values of trigonometric functions at various angles. We know this because the angle is the reference angle for . Because we know that the sine function is negative in the third quadrant, we know the whole answer: sin( ) = - sin( )

What is standard position in trigonometry?

Standard position of an angle - trigonometry
In trigonometry an angle is usually drawn in what is called the "standard position" as shown below. In this position, the vertex of the angle (B) is on the origin of the x and y axis. The other side of the angle is called the terminal side.

What are terminal angles?

Standard Position of an Angle - Initial Side - Terminal Side. An angle is in standard position in the coordinate plane if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

What are Quadrantal angles?


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°

What is the reference angle of 300 degrees?

The reference angle for 300 is 60 degrees.

Why are there infinite Coterminal angles?

Any angle has infinitely many coterminal angles because each time we add360° to that angle—or subtract360° from it—the resulting value has a terminal side in the same location. For example,100° and460° are coterminal for this reason, as is−260°.

Which angle is Coterminal with 120?

120° and -240° Coterminal Angles
Illustration showing coterminal angles of 120° and -240°.

What is the Coterminal angle of 420?

Subtract 360° 360 ° from 420° 420 ° . The resulting angle of 60° 60 ° is positive, less than 360° 360 ° , and coterminal with 420° 420 ° .

What does Coterminal mean?


Definition of coterminal. : having different angular measure but with the vertex and sides identical —used of angles generated by the rotation of lines about the same point in a given line whose values differ by an integral multiple of 2π radians or of 360°coterminal angles measuring 30° and 390°

What is Coterminal angles examples?

Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330° and 390° are all coterminal (see figure 2.1 below).

Which angle is Coterminal with 590?

Subtract 360° 360 ° from 590° 590 ° . The resulting angle of 230° 230 ° is positive, less than 360° 360 ° , and coterminal with 590° 590 ° .

How do you find the complement of an angle?

To determine the supplement, subtract the given angle from 180. 180 - 43 = 137° The supplement of 43° is 137°. To determine the complement, subtract the given angle from 90. 90 - 43 = 47° The complement of 43° is 47°.

Which angles are Coterminal with 3pi 2?

Which angles are coterminal with 3pi/2? The answer choices are: 11pi/2 -pi/2 Pi/2 -7pi/2 - Brainly.com.

What is Coterminal with?


Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal.

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.

What is the reference angle of 90 degrees?

Reference angle for 90°: 90° (π / 2)