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
`(3\pi)/(4)`

angle
`(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 (3\pi)/(4) =\sin (\pi)/(4) = (1)/( √(2) ) \\ \\ \csc(3\pi)/(4)= (1)/(\sin(3\pi)/(4)) = (1)/((1)/( √(2) )) = √(2) \\ \\ \cos(3\pi)/(4) =-\cos (\pi)/(4) = -(1)/( √(2) ) \\ \\ \sec(3\pi)/(4)= (1)/(\cos(3\pi)/(4)) = (1)/(-(1)/( √(2) )) =- √(2) \\ \\ \tan(3\pi)/(4) =-\tan (\pi)/(4) = -1 \\ \\ \cot(3\pi)/(4)= (1)/(\tan(3\pi)/(4)) = (1)/(-1) =- 1`