Unit circle

Standard - CCSS F-TF 2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

The Final FourThe remaining four trigonometric functions (Tangent, Cosecant, Secant, and Cotangent) can all be found using some combination of Sine and/or Cosine using division.

DefinitionA unit circle is a circle with a radius of one (a unit radius). In trigonometry, the unit circle is centered at the origin. For the point (x,y) in Quadrant I, the lengths x and y become the legs of a right triangle whose hypotenuse is 1.

Sine and CosineSine is represented by the vertical leg (y-axis).Cosine is represented by the horizontal leg (x-axis).All Trigonometric Functions are evaluated in response to a reference angle (labeled using the greek symbol for "theta" in the image).

David Leon

References

Bautista, Michael. "Unit Circle Song." YouTube. YouTube, 17 Aug. 2012. Web. 25 Mar. 2015. David. "Unit Circles Are Fun." Heritage School Math. 2011. JPEG File. "The Unit Circle." Precalculus Review Calculus Preview. N.p., n.d. Web. 24 Mar. 2015. "The Unit Circle and Trig Value Signs." Regentsprep. N.p., n.d. Web. 24 Mar. 2015.