How To Find The Nearest Coterminal Angle?
Asked by: Mr. Hannah Davis B.A. | Last update: March 29, 2022star rating: 4.7/5 (62 ratings)
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 the first Coterminal angle?
How to find a coterminal angle between 0 and 360° (or 0 and 2π)? First, divide one number by the other, rounding down (towards the floor): 420/360 = 1. Then, multiply the divisor by the obtained number (called the quotient): 360 * 1 = 360. Subtract this number from your initial number: 420 - 360 = 60. .
What is the Coterminal of 45?
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.
What is the Coterminal angle of 205?
Illustration showing coterminal angles of 205° and -155°. Coterminal angles are angles drawn in standard position that have a common terminal side.
Coterminal Angles - Positive and Negative, Converting
26 related questions found
What is the Coterminal angle of 120?
Coterminal angles are angles in standard position with the same terminal side. For example, angles measuring 120° and – 240° are coterminal.
What is the Coterminal angle of 40?
Illustration showing coterminal angles of 40° and -320°. Coterminal angles are angles drawn in standard position that have a common terminal side.
What is a 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 the smallest positive Coterminal of 780 ∘?
Trigonometry Examples Find an angle that is positive, less than 360° , and coterminal with 780° . Subtract 360° 360 ° from 780° 780 ° . The resulting angle of 420° 420 ° is positive and coterminal with 780° 780 ° but isn't less than 360° 360 ° . Repeat the step.
What is the Coterminal angle of 60?
Coterminal Angles: How to Find Coterminal Angles in Radians and Degrees Frequently Asked Questions (FAQ) Answers What is the coterminal angle of 60°? Some of the coterminal angles of 60° are 420°, 780°, -300°, and -660°. The formula ∠θ = 60° + 360°n represents the coterminal angles of 60°, where n is an integer. .
What is the Coterminal of 380 degrees?
Trigonometry Examples Find an angle that is positive, less than 360° , and coterminal with 380° . Subtract 360° 360 ° from 380° 380 ° . The resulting angle of 20° 20 ° is positive, less than 360° 360 ° , and coterminal with 380° 380 °.
How do you find the positive and negative Coterminal angles?
For example, −330°and 390°are all coterminal. 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.
What angle is Coterminal to 128?
All angles having a measure of 128° + 360k°, where k is an integer, are coterminal with 128°. A positive angle is 28° + 360°(3) or 1208°.
Which angle is Coterminal with 160?
Trigonometry Examples Add 360° 360 ° to −160° - 160 ° . The resulting angle of 200° 200 ° is positive and coterminal with −160° - 160 °.
Which angle is Coterminal to a 175 angle?
Illustration showing coterminal angles of 175° and -185°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, both angles are labeled with the proper degree measure.
Which angle is Coterminal with 155?
Illustration showing coterminal angles of 155° and -205°. Coterminal angles are angles drawn in standard position that have a common terminal side.
Which angle is Coterminal with a 110 angle?
Trigonometry Examples Add 360° 360 ° to −110° - 110 ° . The resulting angle of 250° 250 ° is positive and coterminal with −110° - 110 °.
What is the Coterminal angle of 135?
Find an angle that is positive, less than 360° , and coterminal with −135° . Add 360° 360 ° to −135° - 135 ° . The resulting angle of 225° 225 ° is positive and coterminal with −135° - 135 ° . Since the angle 180° is in the third quadrant, subtract 180° from 225°.
What is the Coterminal angle of 450?
Trigonometry Examples Subtract 360° 360 ° from 450° 450 ° . The resulting angle of 90° 90 ° is positive, less than 360° 360 ° , and coterminal with 450° 450 °.
What is the Coterminal angle of 130?
230° and -130° Coterminal Angles.
What is the Coterminal angle of 250?
Illustration showing coterminal angles of 250° and -110°. Coterminal angles are angles drawn in standard position that have a common terminal side.
What is the Coterminal angle of 170?
Illustration showing coterminal angles of 170° and -190°. Coterminal angles are angles drawn in standard position that have a common terminal side.
What is the Coterminal angle of 260 degrees?
Trigonometry Examples Find an angle that is positive, less than 360° , and coterminal with −260° . Add 360° 360 ° to −260° - 260 ° . The resulting angle of 100° 100 ° is positive and coterminal with −260° - 260 ° . Since the angle 100° is in the second quadrant, subtract 100° from 180°.
Why do we find Coterminal angles?
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.
What are the negative and positive Coterminal angles of − 225?
Find an angle that is positive, less than 360° , and coterminal with −225° . Add 360° 360 ° to −225° - 225 ° . The resulting angle of 135° 135 ° is positive and coterminal with −225° - 225 °.
What is the Coterminal angle of degrees?
A coterminal angle is an angle that ends at the same location as another angle. For example, 1 degree and 361 degrees are at the same location since the total angles in a circle are 360 degrees.
What angle is Coterminal with 112?
Some of the coterminal angles of 112° are 472°, 832°, -248°, and -608°.
