The Unit Circle and Cosine and Sine Functions
TMM 002 PRECALCULUS (Revised March 21, 2017)
2b. Analyze right triangles. Routine analysis of side lengths and angle measurements using trigonometric ratios/functions as well as the Pythagorean Theorem.*
- The student can solve right triangles numerically using trigonometric ratios and relationships.
- The student can compare similar triangles numerically.
- The student can describe relationships within or between right/similar triangles algebraically using trigonometric ratios and relationships.
Section 1: The Unit Circle and the Cosine and Sine Functions
In this module we will introduce and study the two basic trigonometric functions – Cosine and Sine. As we will see any point in the x-y plane is some (radial) distance r away from the origin on a line through the origin. Since a line through the origin is inclined at some angle θ the coordinates of x and y of any point in the plane can be written in terms r and cosine and sine of the angle θ.
Review: Pythagorean Theorem for right angle triangles, positive and negative angles, radian and degree measures.
- Equation of a circle of radius r and center (0,0e).
- Equation of the Unit Circle
- Reference angle
- Definition of Cosine and Sine
- Domain and Range of the Cosine and Sine Functions