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The steps for finding the reference angle of an angle depending on the quadrant of the terminal side: This angle varies depending on the quadrant’s terminal side.
HOW TO FIND REFERENCE ANGLE HOW TO
We already know how to find the coterminal angles of an angle.Īny angle has a reference angle between 0° and 90°, which is the angle between the terminal side and the x-axis. So we decide whether to add or subtract multiples of 360° (or 2π) to get positive or negative coterminal angles respectively. $$\Theta \pm 360° n$$, where n takes a positive value when the rotation is anticlockwise and takes a negative value when the rotation is clockwise. -690° is the negative coterminal angle of 30°.390° is the positive coterminal angle of 30° and.In one of the above examples, we found that 390° and -690° are the coterminal angles of 30° The coterminal angles can be positive or negative. We will illustrate this concept with the help of an example.Įxample: Find a coterminal angle of $$\frac$$ What are Positive and Negative Coterminal Angles? The coterminal angles of any given angle can be found by adding or subtracting 360° (or 2π) multiples of the angle. Therefore, we do not need to use the coterminal angles formula to calculate the coterminal angles. We can determine the coterminal angle(s) of any angle by adding or subtracting multiples of 360° (or 2π) from the given angle. $$=-690° $$ How to Find Coterminal Angles? Then the corresponding coterminal angle is,įinding Second Coterminal Angle : n = −2 (clockwise) Let us find the first and the second coterminal angles.įinding First Coterminal Angle: n = 1 (anticlockwise) The formula to find the coterminal angles is, $$\Theta \pm 360° n $$ Solution: The given angle is, $$\Theta = 30° $$ To understand the concept, let’s look at an example. Two angles are said to be coterminal if the difference between them is a multiple of 360° (or 2π, if the angle is in radians). The only difference is the number of complete circles. We can therefore conclude that 45°, -315°, 405°, – 675°, 765°,… all form coterminal angles. In the above formula, θ ± 360n, 360n denotes a multiple of 360, since n is an integer and it refers to rotations around a plane. The formula to find the coterminal angles of an angle θ depending upon whether it is in terms of degrees or radians is: What is the Formula of Coterminal Angles? Thus 405° and -315° are coterminal angles of 45°. This corresponds to 45° in the first quadrant.
HOW TO FIND REFERENCE ANGLE FULL
After a full rotation clockwise, 45° reaches its terminal side again at -315°.In the first quadrant, 405° coincides with 45°. After full rotation anticlockwise, 45° reaches its terminal side again at 405°.Since its terminal side is also located in the first quadrant, it has a standard position in the first quadrant. The initial side refers to the original ray, and the final side refers to the position of the ray after its rotation. As a measure of rotation, an angle is the angle of rotation of a ray about its origin. When the angles are rotated clockwise or anticlockwise, the terminal sides coincide at the same angle. They are located in the same quadrant, have the same sides, and have the same vertices. Although their values are different, the coterminal angles occupy the standard position.
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STUDYQUERIES’s online coterminal angle calculator tool makes the calculation faster and displays the coterminal angles in a fraction of a second.Īngles that have the same initial side and share their terminal sides are coterminal angles.