Given Tan t = -4 and csc t > 0, how do you find the other 5 trig function?

1 Answer
Nghi N.
May 5, 2015

Call tan x = t. Use the trig identity: 1 + t^2 = 1/(cos^2 x)
Since tan x is negative and csc x > 0, the arc x must be in Quadrant II of the trig unit circle

cos^2 x = 1/(1 + 16) = 1/17 --> cos x = - 24 (Quadrant II)

sin ^2 x = 1 - cos^2 x = 1 - 0.06 = 0.94 -> sin x = 0.97 (Quadrant II)

cot x = -0.24/0.97 = 0.25

sec x = -4.16

$csc x = 1.03#

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