cos5pi/4 పరిష్కరించండి

$$\cos \frac { 5 \pi } { 4 }$$

మూల్యాంకనం చేయండి

$$-\frac{\sqrt{2}}{2}\approx -0.707106781$$

పరిష్కారం దశలు

Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=\pi and y=\frac{\pi }{4} to obtain the result.

$$\cos(\pi +\frac{\pi }{4})=\cos(\pi )\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\pi )$$

Get the value of \cos(\pi ) from trigonometric values table.

$$-\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\pi )$$

Get the value of \cos(\frac{\pi }{4}) from trigonometric values table.

$$-\frac{\sqrt{2}}{2}-\sin(\frac{\pi }{4})\sin(\pi )$$

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

$$-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(\pi )$$

Get the value of \sin(\pi ) from trigonometric values table.

$$-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\times 0$$

లెక్కలు చేయండి.

$$-\frac{\sqrt{2}}{2}$$