How do you find the exact values of the six trigonometric functions of theta if the terminal side of θ in standard position contains the point (-0.3, -0.4)?

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Answer 1 · 2015-05-02T17:56:11

Sketch a diagram (recognizing the standard 3-4-5 triangle) and fill in trig values based on standard definitions:
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$sin(theta) = (-0.4)/(0.5) = -4/5$

$cos(theta) = (-0.3)/(0.5) = - 3/5$

$tan(theta) = (-0.4)/(-0.3) = 4/3$

$csc(theta)= 1/sin(theta) = -5/4$

$sec(theta)=1/cos(theta) = -5/3$

$cot(theta) = 1/tan(theta) = 3/4$