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04 - What is the Unit Circle? Angle Measure in Degrees, Reference Angles & More.

View more at http://www.MathAndScience.com. In this lesson, you will learn what a unit circle is, why it is important, and how we can use the unit circle to solve problems in trigonometry, calculus, algebra, and engineering. First, we explain that a unit circle is a circle of radius one superimposed onto an xy plane. The degree markings around the edge of the circle are explained. We will learn how to count in the counterclockwise direction which makes positive angles. We also learn to count angles in the clockwise direction to form negative angles with respect to the positive x-axis. Finally, we count around the unit circle in increments of degree measure to find the position of any point on the unit circle. This will be used later to solve problems that involve the sine, cosine, and tangent of an angle in standard position. Standard position means that the initial size of the angle is on the positive x-axis and the terminal side of the angle falls somewhere else on the unit circle.