Solve the equation in the interval $[ 0,2 \pi )$ . $\sin x = \cos x$
A) $x = \frac { \pi } { 4 }$ , $x = \frac { 5 \pi } { 4 }$

B) $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

C) $x = \frac { \pi } { 4 }$, $x = \frac { 7 \pi } { 4 }$

D) $x = \frac { 5 \pi } { 4 }$, $x = \frac { 7 \pi } { 4 }$

E) none

Question

Solve the equation in the interval $[ 0,2 \pi )$ . $\sin x = \cos x$
A) $x = \frac { \pi } { 4 }$ , $x = \frac { 5 \pi } { 4 }$

B) $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

C) $x = \frac { \pi } { 4 }$, $x = \frac { 7 \pi } { 4 }$

D) $x = \frac { 5 \pi } { 4 }$, $x = \frac { 7 \pi } { 4 }$

E) none

Quizplus · Accepted Answer

The equation $\sin x = \cos x$ can be rewritten as $\tan x = 1$, which has solutions at $x = \frac{\pi}{4}$ and $x = \frac{5\pi}{4}$ within the interval $[0, 2\pi)$.

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