How to Find the Terminal Side of an Angle
The terminal side of an angle is a trigonometric term used to describe the line that determines the degree of the angle. This line begins at the origin but can end anywhere on the coordinate plane. The other line, referred to as being in standard position, is fixed along the positive x-axis. Finding the length of the terminal side requires the knowledge of the x and y coordinates of the terminal side. Using this knowledge along with the Pythagorean Theorem, finding the length of the terminal side is a simple, arithmetic operation.
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Instructions
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1
Draw a graph of the angle on a piece of paper. Drop a vertical line from the end point of the terminal side down to the x-axis to form a right triangle.
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2
Set up the Pythagorean Theorem, a^2 + b^2 = c^2, to determine the length of the terminal side. In this case, the x-coordinate is the "a" value and the y-coordinate is the "b" value. For example, if the terminal side ended at the point (3,4), set up the Pythagorean Theorem like this: 3^2 + 4^2 = c^2.
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Solve the equation to find the length of the terminal side. For example, solving for c in the equation 3^2 + 4^2 = c^2 finds: c^2 = 9 + 16 ---> c^2 = 25 ---> c = sqrt(25) = 5. So the length of the terminal side for this angle equals 5.
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