Solve (sin^7pi/2cos^83/2pi+sin^63pi/2cos^5pi/2)

$$( \sin ^ { 7 } \frac { \pi } { 2 } \cos ^ { 8 } \frac { 3 } { 2 } \pi + \sin ^ { 6 } \frac { 3 \pi } { 2 } \cos ^ { 5 } \frac { \pi } { 2 } )$$

Evaluate

$$0$$

Solution Steps

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

$$1^{7}\left(\cos(\frac{3}{2}\pi )\right)^{8}+\left(\sin(\frac{3\pi }{2})\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

Calculate 1 to the power of 7 and get 1.

$$1\left(\cos(\frac{3}{2}\pi )\right)^{8}+\left(\sin(\frac{3\pi }{2})\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

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

$$1\times 0^{8}+\left(\sin(\frac{3\pi }{2})\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

Calculate 0 to the power of 8 and get 0.

$$1\times 0+\left(\sin(\frac{3\pi }{2})\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

Multiply 1 and 0 to get 0.

$$0+\left(\sin(\frac{3\pi }{2})\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

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

$$0+\left(-1\right)^{6}\left(\cos(\frac{\pi }{2})\right)^{5}$$

Calculate -1 to the power of 6 and get 1.

$$0+1\left(\cos(\frac{\pi }{2})\right)^{5}$$

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

$$0+1\times 0^{5}$$

Calculate 0 to the power of 5 and get 0.

$$0+1\times 0$$

Multiply 1 and 0 to get 0.

$$0+0$$

Add 0 and 0 to get 0.

$$0$$

Factor

$$0$$