Evaluate
-\frac{\sqrt{2}}{2}\approx -0.707106781
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\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})
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.
-\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.
-\frac{\sqrt{2}}{2}+\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}+\frac{\sqrt{2}}{2}\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}\times 0
Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.
-\frac{\sqrt{2}}{2}
Do the calculations.
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