How do you find the five remaining trigonometric function satisfying tantheta=5/4, costheta<0?

1 Answer
Nghi N.
Jan 16, 2017

Find values of trig functions

Explanation:

Use trig identity:
1 + tan^2 x = 1/(cos^2 x)
cos^2 x = 1/(1 + tan^2 x)
sin^2 x = 1/(1 + cot^2 x)
In this case:
cos^2 x = 1/(1 + 25/16) = 1/(41/16) = 16/41
cos x = - 4/sqrt41 = - (4sqrt41)/41
Find sin x by the same way:
sin^2 x = 1/(1 + 16/25) = 1/(41/25) = 25/41
sin x = - 5/(sqrt41) (because tan x = 5/4 > 0)
tan x = sin/(cos) = 5/4
cot x = 1/(tan) = 4/5
sec x = 1/(cos) = - sqrt41/4
csc x = 1/(sin) = - sqrt41/5

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