cos(7/8pi)-এর সমাধান করুন

$$\cos ( \frac { 7 } { 8 } \pi )$$

মূল্যায়ন করুন

$$-\frac{\sqrt{\sqrt{2}+2}}{2}\approx -0.923879533$$

সমাধানের ধাপগুলো

Use \cos(x+y)=\cos(x)\cos(y)-\sin(y)\sin(x) where x=\frac{3\pi }{2} and y=\frac{\pi }{4} to obtain the result.

$$\cos(\frac{3\pi }{2}+\frac{\pi }{4})=\cos(\frac{3\pi }{2})\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\frac{3\pi }{2})$$

Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.

$$0\cos(\frac{\pi }{4})-\sin(\frac{\pi }{4})\sin(\frac{3\pi }{2})$$

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

$$0\times \frac{\sqrt{2}}{2}-\sin(\frac{\pi }{4})\sin(\frac{3\pi }{2})$$

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

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\sin(\frac{3\pi }{2})$$

Get the value of \sin(\frac{3\pi }{2}) from trigonometric values table.

$$0\times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\left(-1\right)$$

গণনাটি করুন৷

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