Solve A=|sin(-pi/2)-sin(-pi)|+|sin(pi/2)-sin(-pi/2)|+|sin(pi)-sin(pi/2)|

$$A = | \sin ( \frac { - \pi } { 2 } ) - \sin ( - \pi ) | + | \sin ( \frac { \pi } { 2 } ) - \sin ( \frac { - \pi } { 2 } ) | + | \sin ( \pi ) - \sin ( \frac { \pi } { 2 } ) |$$

Solve for A

$$A=4$$

Steps for Solving Linear Equation

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

$$A=|\sin(\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+|\sin(\pi )-\sin(\frac{\pi }{2})|$$

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

$$A=|\sin(\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+|0-\sin(\frac{\pi }{2})|$$

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

$$A=|\sin(\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+|0-1|$$

Subtract 1 from 0 to get -1.

$$A=|\sin(\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+|-1|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -1 is 1.

$$A=|\sin(\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+1$$

Use the property \sin(-x)=-\sin(x).

$$A=|-\sin(-\frac{-\pi }{2})-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+1$$

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

$$A=|-1-\sin(-\pi )|+|1-\sin(\frac{-\pi }{2})|+1$$

Use the property \sin(-x)=-\sin(x).

$$A=|-1-\left(-\sin(\pi )\right)|+|1-\sin(\frac{-\pi }{2})|+1$$

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

$$A=|-1-0|+|1-\sin(\frac{-\pi }{2})|+1$$

Multiply -1 and 0 to get 0.

$$A=|-1+0|+|1-\sin(\frac{-\pi }{2})|+1$$

Add -1 and 0 to get -1.

$$A=|-1|+|1-\sin(\frac{-\pi }{2})|+1$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -1 is 1.

$$A=1+|1-\sin(\frac{-\pi }{2})|+1$$

Use the property \sin(-x)=-\sin(x).

$$A=1+|1-\left(-\sin(-\frac{-\pi }{2})\right)|+1$$

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

$$A=1+|1-\left(-1\right)|+1$$

Multiply -1 and -1 to get 1.

$$A=1+|1+1|+1$$

Add 1 and 1 to get 2.

$$A=1+|2|+1$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 2 is 2.

$$A=1+2+1$$

Add 1 and 2 to get 3.

$$A=3+1$$

Add 3 and 1 to get 4.

$$A=4$$

Assign A

$$A≔4$$