What are terminal and Coterminal angles?

What are terminal and Coterminal angles?

The initial side of an angle is the ray where the measurement of an angle starts. The terminal side of an angle is the ray where the measurement of an angle ends. Co-terminal angles are angles which when drawn at standard position share a terminal side. For example, 30°, -330°, 390° are all coterminal.

How do you find the Coterminal angle in radians on a calculator?

How to calculate a co terminal angle

1. Let’s assume you are given an angle in radians.
2. First, you must convert the radians to degrees.
3. Last, we need to add 360 degrees to that angle to find an angle that is coterminal with the original angle, so 114.59+360 = 475.59 degrees.
4. Check the answer using the calculator above.

What is a Coterminal angle for pi radians?

Coterminal Angles: In Radians For example, pi/3 radians is the given measure of this angel. Then, to find the positive coterminal angle you would add 2 pi, so it would be 7pi/3. To find the negative coterminal angle you would subtract 2pi from the original angle measure, so it would be -5pi/3.

How do you find both Coterminal angles?

Positive and negative coterminal angles Then just add or subtract 360°, 720°, 1080°… (2π,4π,6π…), to obtain positive or negative coterminal angles to your given angle. For example, if α = 1400°, then the coterminal angle in the [0,360°) range is 320° – which is already one example of a positive coterminal angle.

What are two Coterminal angles for?

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.

What is the smallest positive Coterminal angle to degrees?

The smallest angle will be 299∘ , angle 659∘ (299+360) is also coterminal with -61 degrees, and sucesively.

How many Coterminal angles can an angle have?

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.

Which angles are Coterminal with pi 6?

Trigonometry Examples The resulting angle of 11π6 11 π 6 is positive and coterminal with −π6 – π 6 . Since the angle 11π6 11 π 6 is in the fourth quadrant, subtract 11π6 11 π 6 from 2π .

How do you determine if two Coterminal angles are positive and negative?

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 . Example 1: Find a positive and a negative angle coterminal with a 55° angle.

What are the Coterminal angles for?

In Mathematics, the coterminal angle is defined as an angle, where two angles are drawn in the standard position. Also both have their terminal sides in the same location. For example, the coterminal angle of 45 is 405 and -315. Here 405 is the positive coterminal angle, -315 is the negative coterminal angle.

Which angles are Coterminal with degrees?

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).