Question

Find tan x if sec x = sort 37/6 and sin x <0

Answer 1

tan(x) = -1/6

Explanation:

We can use the relation between tan and sec:

`\displaystyletan(x)=\pm\sqrt{\sec^2{x}-1}\\\\tan(x)=-\sqrt{\left((√(37))/(6)\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{(37-36)/(36)}=\boxed{-(1)/(6)}`

The tangent of x is -1/6.