Solve the equation for exact solutions over the interval [0, 2 $$[ 0,2 \pi )$$
-$\cos x = \sin x$
A) $\left\{ \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
B) $\left\{ \frac { 3 \pi } { 4 } , \frac { 7 \pi } { 2 } \right\}$
C) $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
D) $\left\{ \frac { \pi } { 4 } , \frac { 7 \pi } { 4 } \right\}$

Question

Quizplus · Accepted Answer

The equation $\cos x = \sin x$ can be solved by using the identity $\sin x = \cos(\frac{\pi}{2} - x)$. Setting $\cos x = \cos(\frac{\pi}{2} - x)$ and solving for $x$ gives the solutions $\frac{\pi}{4}$ and $\frac{5\pi}{4}$ within the interval $[0, 2\pi)$.

Solve the Equation for Exact Solutions Over the Interval [0 [0,2π)[ 0,2 \pi )[0,2π)

Solve the Equation for Exact Solutions Over the Interval [0 $[ 0,2 \pi )$