Question

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

Answer 1

Answer:

  tan(x) = -1/6

Step-by-step explanation:

We can use the relation between tan and sec:

  $\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}$

The tangent of x is -1/6.