sin(5/2pi0.5+pi/2)-এর সমাধান করুন

$$\sin ( \frac{ 5 }{ 2 } \pi 0.5+ \frac{ \pi }{ 2 } )$$

মূল্যায়ন করুন

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

সমাধানের ধাপগুলো

\frac{5}{4} পেতে \frac{5}{2} এবং 0.5 গুণ করুন।

$$\sin(\frac{5}{4}\pi +\frac{\pi }{2})$$

\frac{7}{4}\pi পেতে \frac{5}{4}\pi এবং \frac{\pi }{2} একত্রিত করুন।

$$\sin(\frac{7}{4}\pi )$$

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

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

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

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

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

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

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

$$-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\cos(\frac{3\pi }{2})$$

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

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

গণনাটি করুন৷

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