Geometry and Trigonometry


How are angles measured in trigonometry?

Angles in trigonometry are measured using a “circle” on x and y axes—often called circle trig definitions. The radian measure of an angle is any real number θ (theta; see illustration). Take an instance in which θ is greater than or equal to zero (θ ≥ 0): Picture taking a length of string and positioning one end at zero; then stretch the other end to 1 on the x axis, to point P(1, 0); this is also considered the radius of the circle. Then, in a counterclockwise direction, swing the string to another position, Q (x, y). This results in θ being an angle (associated with the central angle) with a vertex O or (0, 0) and passing through points P and Q; and because the string is “1 units” in length all the way around, the point from Q to the vertex O will also be 1. The resulting angle θ is measured in degrees—and defined as a part of the circle’s total number of degrees (a circle has 360 degrees); it can also be translated into radians.


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