TUC - Trigonometry and the Unit Circle Lesson

Trigonometry and the Unit Circle

What is the Unit Circle?  The Unit Circle is a circle with the radius equal to 1 and the center at the origin.

Before we move on, let's review the three trigonometric ratios we learned in Geometry: Sine, Cosine and Tangent.  

 

Let's place a right triangle in the unit circle in quadrant I.

Since the unit circle has a radius = 1, the trigonometric ratios can be written as follows:

$\sin\theta=\frac{y}{r}$ = y

$\cos\theta=\frac{x}{r}$ = x

$\tan\theta=\frac{y}{x}$

Where r represents the radius of the circle r > 0:     $x^2+y^2=r^2$

We use our special right triangles, and our Unit Circle to place important angles and coordinates on the Unit Circle. 

**SPECIAL NOTE** In the video below, the angle in the 3rd quadrant is labeled incorrectly. It should be labeled 225 degrees NOT 215 degrees.

This table shows the trigonometric function values for special cases based on our special right triangles.  

 

Try to complete the unit circle below using the what we just learned. 

 

IMAGES CREATED BY GAVS