Math  /  Word Problems

QuestionFind the other trigonometric functions of θ\theta if sinθ=36\sin \theta=\frac{\sqrt{3}}{6} and cosθ>0\cos \theta>0.

Studdy Solution
Rationalize the denominator.
cotθ=1123×33=336\cot \theta = \frac{\sqrt{11}}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{33}}{6}So, the exact values of the trigonometric functions arecosθ=1112,tanθ=23311,cscθ=23,secθ=121111,cotθ=336\cos \theta = \frac{\sqrt{11}}{12}, \tan \theta = \frac{2\sqrt{33}}{11}, \csc \theta =2\sqrt{3}, \sec \theta = \frac{12\sqrt{11}}{11}, \cot \theta = \frac{\sqrt{33}}{6}

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