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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