Find the sine and cosine values at specific angles on the unit circle

To find the sine and cosine values at specific angles on the unit circle, we use the definitions of sine and cosine in terms of the unit circle.

For example, at an angle of 30 degrees (or $\frac{\pi}{6}$ radians):

$ \sin(\frac{\pi}{6}) = \frac{1}{2} $

$ \cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2} $

Let’s find the sine and cosine values for an angle of 45 degrees (or $frac{pi}{4}$ radians):

$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $

$ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $

For an angle of 60 degrees (or $frac{pi}{3}$ radians):

$ sin(frac{pi}{3}) = frac{sqrt{3}}{2} $

$ cos(frac{pi}{3}) = frac{1}{2} $

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