Solve the equation on the interval $$0 \leq \theta

Question

Solve the equation on the interval $$0 \leq \theta < 2 \pi \text {. }$$
-$\cos \theta + \sin \theta = 0$
A) $\frac { 3 \pi } { 4 }$

B) $\frac { 3 \pi } { 2 }$

C) $\frac { 3 \pi } { 4 } , \frac { 7 \pi } { 4 }$

D) $- \frac { \pi } { 6 } , \frac { 2 \pi } { 3 }$

Quizplus · Accepted Answer

To solve the equation $\cos \theta + \sin \theta = 0$, we can square both sides and use the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, but a more straightforward method is to divide both sides by $\cos \theta$ (assuming $\cos \theta \neq 0$), yielding $\tan \theta = -1$. This equation is true for angles where the tangent is -1, which occurs at $\theta = \frac{3\pi}{4}$ and $\theta = \frac{7\pi}{4}$ within the given interval $0 \leq \theta < 2\pi$.

Solve the Equation on the Interval 0≤θ<2π. 0 \leq \theta < 2 \pi \text {. }0≤θ<2π.

Solve the Equation on the Interval $0 \leq \theta < 2 \pi \text {. }$