Question

Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

Answer 1

`cos(\theta)=-(√(35) )/(6)`

Explanation:

Recall the negative angle identity for the sine function:

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

Then, we can find the value of
`sin(\theta)`:

`sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-(1)/(6) )\\sin(\theta)= (1)/(6)`

Now recall the definition of the tangent function:

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

Therefore, now that we know the value of
`sin(\theta)`, we can solve in this equation for
`cos(\theta)`

`tan(\theta)=(sin(\theta))/(cos(\theta))\\-(√(35) )/(35) =(1/6)/(cos(\theta)) \\cos(\theta)=-((1)/(6) )/((√(35) )/(35) ) \\cos(\theta)=-(35)/(6\,√(35) ) \\cos(\theta)=-(√(35) )/(6)`