The reference angle calculator helps you find the acute (smaller than 90 degrees) angle in the standard position between the terminal side and the x-axis of an angle. This reference angle simplifies trigonometric calculations and helps to determine the positive or negative nature of trigonometric functions.
A reference angle is the positive acute angle formed between the terminal side of an angle and the nearest x-axis in a Cartesian coordinate system.
In other words, the reference angle is that angle sandwiched between the terminal side and the x-axis and it always falls between 0 and 90 degrees.
Let’s say you are hiking on a hill. The slope of the hill is 65 degrees from the horizontal ground. So, find the in terms of degree.
To find the reference angle in degrees, you can use the formula:
Reference Angle = 90 degrees - Angle of Slope
In this case, the angle of the slope is 65 degrees. Plug this value into the formula:
Reference Angle = 90 degrees - 65 degrees = 25 degrees
So, the reference angle in degrees for this hill is 25 degrees. This tells you that the slope of the hill is 25 degrees away from being completely vertical (90 degrees from the horizontal ground).
The reference angle calculator enables you to input any angle and determine its corresponding reference angle, which is an acute angle. If you don’t want to indulge in formulas and complex calculations then just try the calculator:
Trigonometric functions can be evaluated for angles outside the first quadrant using reference angles. Additionally, they can be used to find the (x,y) coordinates of those angles.
In order to find the reference angle we always find the difference between 225˚ and 180˚. It is important to note that the reference angle can never be negative.
Cuemath.com: Reference Angle, Reference Angle Definition, How to Draw Reference Angle? Rules for Reference Angles in Each Quadrant, How to Find Reference Angles? and Steps to Find Reference Angles.
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