Solve the equation. Give a general formula for all the solutions.
-$$\tan \theta = - 1$$
A) $\theta = \frac { 3 \pi } { 4 } + k \pi$
B) $\theta = \frac { \pi } { 4 } + k \pi$
C) $\theta = \frac { \pi } { 4 } + 2 k \pi$
D) $\theta = \frac { 3 \pi } { 4 } + 2 k \pi$

Question

Quizplus · Accepted Answer

The equation $\tan \theta = -1$ has solutions where $\theta$ is an odd multiple of $\frac{\pi}{4}$, specifically at $\frac{3\pi}{4}$, $\frac{7\pi}{4}$, etc. The general solution is $\theta = \frac{3\pi}{4} + k\pi$, where $k$ is any integer, because the tangent function has a period of $\pi$.

Solve the Equation tan⁡θ=−1\tan \theta = - 1tanθ=−1 A) θ=3π4+kπ\theta = \frac { 3 \pi } { 4 } + k \piθ=43π​+kπ

Solve the Equation $\tan \theta = - 1$ A) $\theta = \frac { 3 \pi } { 4 } + k \pi$