Question

Find the values of the other five trigonometric functions in each of the following:

(i) cot x = 12/5, x in quadrant III

(ii) cos x = -1/2, x in quadrant II

(iii) tan x = 3/4, x in quadrant III

(iv) sin x = 3/5, x in quadrant I


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Answer 1

Given that cos(t) = -3/5

a) sin(t)

Then sin2(t) + cos2(t) = 1

Substitute cos(t) value

sin2(t)+ ( -3/5)2= 1

sin2(t) = 1- 9/25

sin(t) = √ 16/25

Therefore sin(t) = 4/5

b) tan(t)

tan(t) = sin(t)/cos(t)

(4/5)/(-3/5) = - 4/3

Therefore tan(t) = - 4/3

Therefore sin(t) = 4/5 and tan(t) = -4/3.