Question

Consider this equation. Cos(0) = 8/9 if 0 is an angle in quadrant IV, what is the value of tan(0)? I

Answer 1

Answer:

$\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}$

Step-by-step explanation:

We are given that:

$\displaystyle \cos(\theta)=\frac{8}{9}$

Where θ is in QIV.

And we want to find the value of tan(θ).

Recall that cosine is the ratio of the adjacent side over the hypotenuse.

Therefore, the opposite side is:

$o=\sqrt{9^2-8^2}=\sqrt{17}$

Next, in QIV, only cosine is positive: sine and tangent are both negative.

Tangent is the ratio of the opposite side to the adjacent. So:

$\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Substitute. Tangent is negative in QIV. Hence:

$\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}$