Question

Find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.) 3Ï 4

Answer 1

Given the angle $\frac{3\pi}{4}$

angle $\frac{3\pi}{4}$ is equivalent to angle 135 degrees and angle 135 degrees is equvalent to angle 45 degrees in the second quadrant, thus sine is positive but cosine and tangent are negative.

$\sin \frac{3\pi}{4} =\sin \frac{\pi}{4} = \frac{1}{ \sqrt{2} } \\ \\ \csc\frac{3\pi}{4}= \frac{1}{\sin\frac{3\pi}{4}} = \frac{1}{\frac{1}{ \sqrt{2} }} = \sqrt{2} \\ \\ \cos\frac{3\pi}{4} =-\cos \frac{\pi}{4} = -\frac{1}{ \sqrt{2} } \\ \\ \sec\frac{3\pi}{4}= \frac{1}{\cos\frac{3\pi}{4}} = \frac{1}{-\frac{1}{ \sqrt{2} }} =- \sqrt{2} \\ \\ \tan\frac{3\pi}{4} =-\tan \frac{\pi}{4} = -1 \\ \\ \cot\frac{3\pi}{4}= \frac{1}{\tan\frac{3\pi}{4}} = \frac{1}{-1} =- 1$