5. the graph of $y = \\tan x$ is shown. the dashed line represents $y = -\\sqrt{3}$. find the exact…
5. the graph of $y = \\tan x$ is shown. the dashed line represents $y = -\\sqrt{3}$. find the exact coordinates of point a.
Answer
Explanation:
Step1: Set up the equation
$\tan x = -\sqrt{3}$
Step2: Find reference angle
$\tan \theta = \sqrt{3} \implies \theta = \frac{\pi}{3}$
Step3: Locate x in correct interval
Point A is between $\frac{\pi}{2}$ and $\pi$, so $x = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$
Step4: Identify y-coordinate
The dashed line is $y = -\sqrt{3}$, so $y = -\sqrt{3}$
Answer:
$\left(\frac{2\pi}{3}, -\sqrt{3}\right)$