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ludmilkaskok [199]
3 years ago
10

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

Mathematics
1 answer:
Sveta_85 [38]3 years ago
6 0

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.

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