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

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

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

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

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

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