Math  /  Trigonometry

QuestionEvaluate (if possible) the sine, cosine, and tangent at the real number tt. (If an answer is undetined, t=π3t=\frac{\pi}{3} sint=\sin t= \square cost=\cos t= \square tant=\tan t= \square

Studdy Solution
Evaluate the tangent of t t using the sine and cosine values.
The tangent is defined as the ratio of sine to cosine:
tan(π3)=sin(π3)cos(π3) \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\frac{\pi}{3}\right)}
Substitute the known values:
tan(π3)=3212 \tan\left(\frac{\pi}{3}\right) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}
Simplify the expression:
tan(π3)=3 \tan\left(\frac{\pi}{3}\right) = \sqrt{3}
The values are:
sint=32\sin t = \frac{\sqrt{3}}{2} cost=12\cos t = \frac{1}{2} tant=3\tan t = \sqrt{3}

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