Solve the trigonometric equation for all values $0 \leq x< 2 \pi$.
\[
\cot x+1=0
\]

Answer

Expert–verified

Hide Steps

Answer

$\boxed{x = \frac{3\pi}{4}}$

Steps

Step 1 ：Rewrite the equation as: $ \frac{1}{\tan x} + 1 = 0 $

Step 2 ：Solve for $\tan x$ to get $\tan x = -1$

Step 3 ：Find the value of x in the range $0 \leq x < 2\pi$ that satisfies the equation: $x = \frac{3\pi}{4}$

Step 4 ：$\boxed{x = \frac{3\pi}{4}}$