


TrigonometryDegrees and RadiansMeasurement of Angles
On a Cartesian coordinate system, we draw a circle centred at the origin and with radius 1. Let P be a point on the circle. The line OP and the positive xaxis form an angle Let us agree that an angle measured counterclockwise is positive, and an angle measured clockwise is negative. (See diagram below.)
DegreesStarting from the positive xaxis, the point P travels around the circle in a counterclockwise manner.
If the point travels clockwise, when it hits the negative yaxis its angle will measure 90° and when it hits the negative xaxis its angle will measure 180°.
Exercise 1.
RadiansIf the length of the arc from (1, 0) to P is 1unit we say the angle is 1 radian ( rad in short). When the unit of an angle is absent, we assume it is in radians. The circumference of the circle of radius 1 is 2π or 2π radians. So, measuring counterclockwise, 2π = 360° and π = 180°. This provides us with the following conversion formulas for changing between degrees D and radians R: oror
Exercise 2.
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