Question

Given the following use a Pythagorean identity to find tan(0) if 0 is in quadrant IV

Answer 1

A. -3√7/7

Explanation:

We have the equation in trigonometry as following:

with (cos x)^2 different from 0, we have:

`(1)/(cos^(2)x ) = 1 + tan^(2) x`

=>
`tan^(2) x = (1)/(cos^(2)x ) -1`

As (cos θ) = √7/4 ≠ 0, so that we can replace θ into the above equation, we could have:

(tan θ)^2 = 1/[(cos θ)^2] -1

=> (tan θ)^2 =
`(1)/((√(7)/4) ^(2) ) -1 = (1)/(7/16) - 1`

=>(tan θ)^2 = 16/7 - 7/7 = 9/7

=> tan θ = (3√7)/7

or tan θ = - (3√7)/7

As θ is in quadrant IV, so that its tangent has negative value

=> tan θ = -3√7/7

So that the correct answer is A