Respuesta :
Answer:
pi/4 and 7pi/4.
Step-by-step explanation:
Sin 3pi/4 is in the second quadrant and is positive and has the same value as sin pi/4.
Sin (3pi/4) = sin (pi/4) = cos pi/4.
Also as cos x is positive in the 4th quadrant cos (2pi - pi/4)
= cos 7pi/4 is also equal to sin 3pi/4.
Answer:
[tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex]
Step-by-step explanation:
Angle [tex]\frac{3\pi}{4}[/tex] lies in second quadrant in which [tex]\sin[/tex] is positive .
[tex]\sin \left ( \frac{3\pi}{4} \right )\\=\sin \left ( \pi-\frac{\pi}{4} \right )\\=\sin \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]
We know that [tex]\cos[/tex] is positive in first and fourth quadrant .
In first quadrant :
We know that angle [tex]\frac{\pi}{4}[/tex] lies in first quadrant .
[tex]\cos \left ( \frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}[/tex]
In fourth quadrant :
We know that angle [tex]\frac{3\pi}{4}[/tex] lies in fourth quadrant.
[tex]\cos \left ( \frac{7\pi}{4} \right )\\=\cos \left ( 2\pi-\frac{\pi}{4} \right )\\=\cos \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]
So, for angles [tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex] , [tex]\cos x[/tex] has the same value as [tex]\sin \left ( \frac{3\pi}{4} \right )[/tex]
