Given sin (-θ) = 1/5 and tanθ=√6/12.

What is the value of cosθ?

A). √6/60

B). - 2√6/5

C). - √6/60

D). 2√6/5

B). - 2√6/5

Step-by-step explanation:

tan theta = sin theta / cos theta

Multiply each side by cos theta

tan theta * cos theta = sin theta

Divide each side by tan theta

cos theta = sin theta / tan theta

We know that the sin ( - theta) = - sin theta since sin is and odd function

sin theta = - (sin (-theta))

Putting this into the above equation,

cos theta = - (sin (-theta)) / tan theta

cos theta = - 1/5 / (sqrt (6) / 12)

Remember when dividing fractions, we use copy dot flip

cos theta = - 1/5 * 12 / sqrt (6)

cos theta = - 12 / (5 sqrt (6))

We cannot leave a sqrt in the denominator, so multiply the top and bottom by sqrt (6) / sqrt (6)

cos theta = - 12 / (5 sqrt (6)) * sqrt (6) / sqrt (6)

cos theta = - 12 sqrt (6) / 5*6

Simplify the fraction.

cos theta = - 2 sqrt (60/5