Answer:
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
