Find tan θ if sec θ = √26 ÷ 5 and sin θ < 0?

Solution:

sec θ = √26/5

So we know that

cos θ = 5/√26

sin θ < 0 (Given)

Which means the reference angle is in IV Quadrant where sin θ < 0 and cos θ > 0

So we get

sin θ = - √(1 - cos²θ)

Substituting the value of cos θ

sin θ = - √(1 - 25/26)

Taking LCM

sin θ = - √1/26

sin θ = - 1/√26

We know that

tan θ = sin θ/ cosθ

So we get

tan θ = [- 1/√26]/ [5/√26]

tan θ = -1/5

Therefore, tan θ = -1/5.

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Find tan θ if sec θ = √26 ÷ 5 and sin θ < 0?

Summary:

if sec θ = √26 ÷ 5 and sin θ < 0, tan θ = -1/5.