How do you evaluate the six trigonometric functions given t=5π/4?

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Answer 1 · 2018-03-16T08:43:04

As below.

To find 6 trigonometric functions of #(5pi) / 4#

#hat (5pi)/4 # is #> 180^@# & < #270^@# Hence it falls in the third quadrant where only #tan theta and cot theta# positive#

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#sin (5pi)/4 = sin (pi + pi/4) = - sin (pi/4) = color(red)(- (1/sqrt2)#

#csc (5pi)/4 = csc (pi + pi/4) = - csc (pi/4) = color(red)(- (sqrt 2)#

#cos (5pi)/4 = cos (pi + pi/4) = - cos (pi/4) =color(red)( - (1/sqrt2)#

#sec (5pi)/4 = sec (pi + pi/4) = - sec (pi/4) = color(red)(- (sqrt2)#

#tan (5pi)/4 = tan (pi + pi/4) = tan (pi/4) = color(green)(1 #

#cot (5pi)/4 = cot (pi + pi/4) = cot (pi/4) = color(green)(1#