Finding the Tangent of Angles on the Unit Circle
Answer 1
Olivia Lee
To find the tangent of an angle θ on the unit circle, we use the definition of tangent in terms of sine and cosine: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$
Consider the angle θ = 45 degrees. The coordinates on the unit circle are (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}). Therefore,
$\tan(45°) = \frac{\sin(45°)}{\cos(45°)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $
Answer 2
Isabella Walker
To find the tangent of an angle θ on the unit circle, we use the relation: $ an( heta) = frac{sin( heta)}{cos( heta)}$
Consider the angle θ = 30 degrees. The coordinates on the unit circle are (frac{sqrt{3}}{2}, frac{1}{2}). Therefore,
$ an(30°) = frac{sin(30°)}{cos(30°)} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} =frac{sqrt{3}}{3} $
Answer 3
Emma Johnson
To find the tangent of an angle θ on the unit circle, use: $ an( heta) = frac{sin( heta)}{cos( heta)}$
Consider the angle θ = 60 degrees. The coordinates on the unit circle are (frac{1}{2}, frac{sqrt{3}}{2}). Therefore,
$ an(60°) = frac{sin(60°)}{cos(60°)} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3} $
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