Trigonometric Ratios in the Unit Circle

Now, recall sine, cosine and tangent from the previous lesson. When you learned about them, we only used acute angles, but now we want to be able to apply those concepts to any angle on the plane. So, we are going to generalize the definitions to those below:

unit circle with angle theta and plot (x, y)

unit circle with angle theta and point (-x, -y)

Sine: the ratio of y to r: equation image indicator $LaTeX: \sin\theta=\frac{y}{r}$

Cosine: the ratio of x to r: equation image indicator $LaTeX: \cos\theta=\frac{x}{r}$

Tangent: the ratio of y to x: equation image indicator $LaTeX: \tan\theta=\frac{y}{x}$

Where r represents the radius of the circle r > 0:

Watch the video below to learn about how to use the trig ratios:

We are dealing with a unit circle, so the radius is equal to 1, therefore cos(theta)= x and sin(theta)=y The reason the Unit Circle is so important is because the radius is 1. So our new ratios become: equation image indicator and

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