Answer:
[tex]\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos(\theta)=\frac{8}{9}[/tex]
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:
[tex]o=\sqrt{9^2-8^2}=\sqrt{17}[/tex]
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:
[tex]\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute. Tangent is negative in QIV. Hence:
[tex]\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}[/tex]
