Q:

# How do you use a unit circle with tangent chart?

A:

A unit circle can help solve values for the tangent of angles 30 degrees, 45 degrees and 60 degrees. Tan (θ) = x/y, sin (θ) = y and cos (θ) = x. By substituting x and y, tan (θ) = sin (θ)/cos (θ).

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The unit circle has a radius of 1, sin 30 = 1/2 and cos 30 = (√3)/2; thus, tan 30 = (1/2)/ (√3)/2 or √3/3. Tan 45 = ((√2)/2)/ ((√2)/2) or 1 and tan 60 = (√3)/2/ 1/2 or √3. While cos 90 = 0 and sin 90 = 1 tan 90 is unknown.

In trigonometry, the size of the angle theta is most important.

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