P is a point on the terminal side of θ in standard position, how do you find the exact value of the six trigonometric functions for θ P(–8, –8)?

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Answer 1 · 2015-05-08T04:21:14

If O is the origin, the angle (Ox, OP) is $\frac{5 π}{4}$ $(5pi)/4$ or 225 deg.

$sin 225 = sin (180 + 45) = - sin 45 = - \frac{s q r 2}{2}$ $sin 225 = sin (180 + 45) = -sin 45 = -(sqr2)/2$

$cos 225 = cos (180 + 45) = - cos 45 = - s q r \frac{2}{2}$ $cos 225 = cos (180 + 45) = -cos 45 = -sqr2/2$

tan 225 = tan 45 = 1

cot 225 = 1

$sec 225 = \frac{1}{cos 225} = - \frac{2}{s q r 2} = - s q r 2$ $sec 225 = 1/cos 225 = -2/(sqr2) = -sqr2$

$csc 225 = \frac{1}{sin 225} = - s q r 2$ $csc 225 = 1/sin 225 = -sqr2$