Find the tangent of the angle $ heta $ in the unit circle
Answer 1
Olivia Lee
Consider the unit circle, where the radius is 1. Let $ \theta $ be an angle in standard position.
The coordinates of the point on the unit circle at an angle $ \theta $ are $(\cos \theta, \sin \theta)$.
The tangent of the angle $ \theta $ is given by
$ \tan \theta = \frac{\sin \theta}{\cos \theta} $
For example, if $ \theta = 45^\circ $, then $ \sin 45^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2} $.
Thus, $ \tan 45^\circ = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $
Answer 2
Thomas Walker
On the unit circle, the coordinates of a point corresponding to an angle $ heta $ are $(cos heta, sin heta)$.
The tangent of $ heta $ can be determined using the formula
$ an heta = frac{sin heta}{cos heta} $
If $ heta = 30^circ $, then $ sin 30^circ = frac{1}{2} $ and $ cos 30^circ = frac{sqrt{3}}{2} $.
Thus,
$ an 30^circ = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3} $
Answer 3
Samuel Scott
For a point on the unit circle at angle $ heta $,
$ an heta = frac{sin heta}{cos heta} $
If $ heta = 60^circ $,
$ sin 60^circ = frac{sqrt{3}}{2}, cos 60^circ = frac{1}{2} $
Thus,
$ an 60^circ = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3} $
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