Question

Determine the values of each of the other 5 trig functions cosθ= -1/4, tanθ > 0

Answer 1

EXPLANATION

Given the function cos theta = -1/4

`\sin ^2x=1-\cos ^2x=1-(1)/(16)=\text{ }(15)/(16)=0.9375=>\text{ }\sin x=0.9682`

Let's calculate tan x:

`\tan \text{ x = }(\sin x)/(\cos x)=\text{ }(0.9682)/(-0.25)=-3.8728`
`\cot \text{ x = }\frac{1}{\tan \text{ x}}=\text{ }(1)/(-3.8728)=\text{ -0.2582}`
`\sec \text{ x = }\frac{1}{\text{cos x }}=\text{ }-4`
`co\sec \text{ x =}(1)/(0.9682)=\text{ 1.0328}`