 # Special Triangles & Unit Circle

Related Topics:
Common Core (Functions)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

Common Core: HSF-TF.A.3

The following diagram shows the unit circle for radians and degrees. Scroll down the page for more examples and solutions for trigonometric functions using the unit circle. Introduction to Trigonometric Functions Using Triangles
Defines trigonometric functions using right triangles. Sine, Cosine, and Tangent of π/3, π/4, π/6
This video demonstrates geometrically the values of Sine, Cosine, and Tangent for angles with radian measures π/3, π/4, π/6.

Trig Values of Special Angles F.TF.3
Find the trigonometric function values at critical angles between 0 and π/2, and use the unit circle to find trigonometric values at intervals of π (tangent) or 2π (sine and cosine) beyond them.
Deriving Values on the Unit Circle
Derive the values in the first quadrant of the unit circle using geometry and the pythagorean theorem. A way to remember the Entire Unit Circle for Trigonometry

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  