# 7: Trigonometry

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## Learning Objectives

• Sketch angles in standard position measured in either degrees or radians.
• Identify coterminal angles and produce a sketch.
• Identify reference angles and produce a sketch.
• Use the equation of a circle to compute points on the circle as ordered pairs.
• Understand how special right triangles, together with symmetry, yields the ordered pairs on the unit circle.

• 7.1: The Unit Circle
The core concepts of trigonometry are developed from a circle with radius equal to 1 unit, drawn in the xy-coordinate plane, centered at the origin. This circle is given a name: the unit circle. An angle is in standard position if its initial side is along the positive x-axis and its vertex is at the origin: point (0,0). An angle that rotates in the counter-clockwise direction is a positive angle. An angle that rotates in the clockwise direction is a negative angle.
• 7.2: Reference Angles
A reference angle is the positive acute angle between the terminal side of the standard angle and the x-axis. The word reference is used because all angles can refer to QI. That is, memorization of ordered pairs is confined to QI of the unit circle. If a standard angle has a reference angle of 30˚, 45˚, or 60˚, the unit circle's ordered pair is duplicated, but the sign value of x or y may need adjustment, depending on the quadrant of the terminal side of the standard angle.