Questions: Use a graph to solve the given equation for -2 π ≤ x ≤ 2 π. 10 tan x = -10 x = (Type an integer or a simplified fraction in terms of π. Use a comma to separate answers as needed.

$Use a graph to solve the given equation for -2 π ≤ x ≤ 2 π. 10 tan x = -10 x = (Type an integer or a simplified fraction in terms of π. Use a comma to separate answers as needed.$

Transcript text: Use a graph to solve the given equation for $-2 \pi \leq x \leq 2 \pi$. \[ \begin{array}{l} 10 \tan x=-10 \\ x=\{ \} \end{array} \] $\square$ (Type an integer or a simplified fraction in terms of $\pi$. Use a comma to separate answers as needed.

Solution

Solution Steps

Step 1: Solve the equation

Given the equation: \[ 10 \tan x = -10 \] We can simplify it to: \[ \tan x = -1 \]

Step 2: Find the solutions within the given range

The general solution for $\tan x = -1$ is: \[ x = -\frac{\pi}{4} + n\pi \] where $n$ is an integer.

For the range $-2\pi \leq x \leq 2\pi$, we find the specific solutions: \[ x = -\frac{\pi}{4}, \frac{3\pi}{4}, -\frac{5\pi}{4}, \frac{7\pi}{4} \]

Final Answer

The solutions are: \[ x = \left\{ -\frac{\pi}{4}, \frac{3\pi}{4}, -\frac{5\pi}{4}, \frac{7\pi}{4} \right\} \]

{"axisType": 3, "coordSystem": {"xmin": -6.2832, "xmax": 6.2832, "ymin": -10, "ymax": 10}, "commands": ["y = 10tan(x)", "y = -10"], "latex_expressions": ["$y = 10\\tan(x)$", "$y = -10$"]}

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