Question

Given sin(−θ)=−1/4 and tanθ=√15/15 . What is the value of cosθ ?

Answer 1

`\cos \theta = (√(15))/(4)`

Explanation:

The sine function is an odd function, that is:

`\sin (-\theta) = - \sin \theta`

Then,

`\sin \theta = (1)/(4)`

The cosine function is computed by the following relation:

`\cos \theta = (\sin \theta)/(\tan \theta)`

`\cos \theta = ((1)/(4) )/((√(15))/(15) )`

`\cos \theta = ((1)/(4) )/((1)/(√(15)) )`

`\cos \theta = (√(15))/(4)`

Answer 2

`\cos\left(\theta\right)=(√(15))/(4)`

Explanation:

Given that
`\sin\left(-\theta\right)=-(1)/(4)` and
`\tan\left(\theta\right)=(√(15))/(15)`

Using those values we need to find value of
`\cos\left(\theta\right)`

So let's begin with equation of
`\tan\left(\theta\right)=(√(15))/(15)` and simplify it to get value of
`\cos\left(\theta\right)`

`\tan\left(\theta\right)=(√(15))/(15)`

`(\sin\left(\theta\right))/(\cos\left(\theta\right))=(√(15))/(15)`

`\sin\left(\theta\right)=(√(15))/(15)\cos\left(\theta\right)`

`\sin\left(\theta\right)\cdot(15)/(√(15))=\cos\left(\theta\right)`

`\cos\left(\theta\right)=\sin\left(\theta\right)\cdot(15)/(√(15))`

`\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot(15)/(√(15))` {since
`\sin\left(-\theta\right)=-\sin\left(\theta\right)` }

`\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot√(15)`

`\cos\left(\theta\right)=-\left(-(1)/(4)\right)\cdot√(15)`

`\cos\left(\theta\right)=(√(15))/(4)`