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Reference Angles and Triangles

HSF-TF.C.8
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High School Functions - HSF-TF.C.8

What are Reference Angles in Trigonometry? When the terminal side of the angle makes the smallest angle with the x-axis, that is what we call reference angles in trigonometry. The value of the angle is always positive, regardless of the quadrant in which it lies and is always less than 90˚. It can be equal to 90˚, but it can never be greater, even for large angles. It is useful when using trigonometric functions. When angles have the same reference angles, they give the same trigonometric function values. It eliminates the need to memorize trigonometric function values for angles less than or equal to 90˚. It is very easy to find reference angles. When dealing with large angles, you need to subtract 360˚ from it until you get an angle between 0˚ and 360˚. For negative angles, you add 360˚, until you get an angle within the range from 0˚ to 360˚. You can then sketch the angle to determine which quadrant the reference angle lies in. If the angle lies in the 1st quadrant, it is the reference angle. If it lies in the second quadrant, you subtract the angle from 180˚. For the third quadrant, you subtract 180˚ from the angle, and for the fourth quadrant, you subtract 360˚ from the angle. Students learn how to use and manipulate known values of angles to determine other values in the same system.

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