Solve {left(sin(pi/2)+cos(pi)right)}^2-4cos(2pi)+3sin(2pi)+1

$${ \left( \sin ( \frac{ \pi }{ 2 } ) + \cos ( \pi ) \right) }^{ 2 } -4 \cos ( 2 \pi ) +3 \sin ( 2 \pi ) +1$$

Evaluate

$$-3$$

Solution Steps

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

$$\left(1+\cos(\pi )\right)^{2}-4\cos(2\pi )+3\sin(2\pi )+1$$

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

$$\left(1-1\right)^{2}-4\cos(2\pi )+3\sin(2\pi )+1$$

Subtract 1 from 1 to get 0.

$$0^{2}-4\cos(2\pi )+3\sin(2\pi )+1$$

Calculate 0 to the power of 2 and get 0.

$$0-4\cos(2\pi )+3\sin(2\pi )+1$$

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

$$0-4\times 1+3\sin(2\pi )+1$$

Multiply 4 and 1 to get 4.

$$0-4+3\sin(2\pi )+1$$

Subtract 4 from 0 to get -4.

$$-4+3\sin(2\pi )+1$$

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

$$-4+3\times 0+1$$

Multiply 3 and 0 to get 0.

$$-4+0+1$$

Add -4 and 0 to get -4.

$$-4+1$$

Add -4 and 1 to get -3.

$$-3$$

Factor

$$-3$$