Question

If cos x= √2/2 and x is a fourth quadrant angle, evaluate tan x

Answer 1

Given that;

`\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ and\text{ x is a fourth angle quadrant.} \end{gathered}`

Note that cosine is positive on the fourth angle quadrant while tangent is negative.

From;

`\begin{gathered} \cos x=\frac{\sqrt[]{2}}{2} \\ \text{adjacent}=\sqrt[]{2},\text{ hypotenuse= 2} \\ \text{opposite}=\text{ }\sqrt[]{2^2-(\sqrt[]{2})^2} \\ \text{opposite}=\sqrt[]{4-2} \\ \text{opposite}=\sqrt[]{2} \\ \end{gathered}`

Thus, the tangent is;

`\begin{gathered} \tan x=\frac{-\sqrt[]{2}}{\sqrt[]{2}} \\ \tan x=-1 \end{gathered}`