Find tan θ if sec θ = √37 divided by 6 and sin θ < 0?

Solution:

sec θ = √37/6 and sin θ < 0 (Given)

We know that 

sec θ = hypotenuse/adjacent

As we know the adjacent side and hypotenuse, we can determine the opposite side using the Pythagorean theorem.

Opposite = √(hypotenuse² - adjacent²)

Substituting the values

Opposite = √[(√37)² - 6²]

= √(37 - 36)

= √1

Opposite = 1

We know that

sin θ = opposite/hypotenuse

= 1/√37 < 0

tan θ = opposite/ adjacent

= 1/6

Therefore, tan θ = 1/6.

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Find tan θ if sec θ = √37 divided by 6 and sin θ < 0?

Summary:

If sec θ = √37 divided by 6 and sin θ < 0, tan θ is 1/6.