Question

Find tan θ if sec θ = square root of thirty seven divided by six and sin θ < 0.

Answer 1

tanx =
`-(1)/(6)`

Explanation:

hey there,

< You have to memorize trigonometric identities for this. Here's the one we'll use for this problem.

`1 + tan^2x=sec^2x`

Plug in the sec since we already know what it is.

`tan^2x = ((√(37) )/(6))^2 -1`

When you square it, you get 37/36. 37/36-1 = 1/36

tan^2x = 1/36

Since it's squared, let's find the square root of 1/36.

It would be +- 1/6.

Since sinx < 0, it has to be -1/6. >

Hope this helped! Feel free to ask anything else.

Answer 2

we know that

sec²θ=tan²θ+1-------> tan²θ=> sec²θ-1
sec θ = (√37)/6

tan²θ=> [(√37)/6]²-1--------> (37/36)-1-------> 1/36
tanθ=√(1/36)--------> 1/6

remember that
sec θ = 1/ cos θ
the cos θ is > 0
and
the sin θ < 0
so the angle θ belong to the fourth quadrant-------> tan θ is negative

therefore

the answer is
tan θ=-1/6