What is a Coterminal angle and reference angle?

Coterminal angles are equal angles. Reference angle is the smallest angle that you can make from the terminal side of an angle with the \(x\)-axis.

What is the definition of Coterminal angle?

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).

What is reference angle?

Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

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∘ .

How do you find the reference angle?

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 a positive and negative Coterminal angle?

One way to find the measure of an angle that is coterminal with an angle θ is to add or subtract integer multiples of 360°. Add 360° to find a positive coterminal angle. Subtract 360° to find a negative coterminal angle. Angles that measure 425° and –295° are coterminal with a 65° angle.

What you mean by angle?

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angle is also used to designate the measure of an angle or of a rotation.

What is the reference angle of 100?

80°
Reference angle for 100°: 80° Reference angle for 105°: 75° Reference angle for 110°: 70°

How do you find the reference angle examples?

Finding Reference Angles Example 1: Find the reference angle for 150 degrees. 180 – 150 = 30 degrees. Therefore, the reference angle is 30 degrees. If the terminal side of the angle is in the third quadrant, we take 180 degrees and subtract it from the angle measure.

How do you find positive and negative angles?

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians .

How do you find positive and negative Coterminal angles?

Find the measures of a positive angle and a negative angle that are coterminal with each given angle. Add 360° to find a positive coterminal angle. Subtract 360° to find a negative coterminal angle.

What are some examples of coterminal angles?

and a terminal side.

How do you find coterminal angles?

We can find the coterminal angles of a given angle by using the following formula: Coterminal angles of a given angle θ may be obtained by either adding or subtracting a multiple of 360° or 2π radians. Coterminal of θ = θ + 360° × k if θ is given in degrees, Coterminal of θ = θ + 2π × k if θ is given in radians.

How do you find reference angle?

So, the reference angle is the angle between the terminal side and the x-axis.Lets find out that angle. And the reference angle is #pi/4#. There is another simpler way to do it. There is a formula to find the reference angle. #pi*n + theta , n in ZZ# where #theta# is your angle.

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°.