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

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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
User Simon Kraus
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