Find all solutions in the interval [0, 2π]
-$\cos x = \sin x$
A) $x = \frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$
B) $x = \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 }$
C) $x = \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 2 }$
D) $x = \frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$

Question

Quizplus · Accepted Answer

The equation $\cos x = \sin x$ can be solved by recognizing that this equality occurs at angles where the two functions have the same value. Since $\sin x = \cos(\frac{\pi}{2} - x)$, the equation implies that $x = \frac{\pi}{2} - x$ or $x = \pi - x$, leading to solutions at $x = \frac{\pi}{4}$ and $x = \frac{5\pi}{4}$ within the given interval [0, 2π].

Find All Solutions in the Interval [0, 2π] - cos⁡x=sin⁡x\cos x = \sin xcosx=sinx

Find All Solutions in the Interval [0, 2π]
- $\cos x = \sin x$