Solve f(pi/3)=2sin(pi/3-pi/2)

$$f ( \frac { \pi } { 3 } ) = 2 \sin ( \frac { \pi } { 3 } - \frac { \pi } { 2 } )$$

Evaluate

$$-1$$

Solution Steps

Combine \frac{\pi }{3} and -\frac{\pi }{2} to get -\frac{1}{6}\pi .

$$2\sin(-\frac{1}{6}\pi )$$

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

$$2\left(-1\right)\sin(\frac{1}{6}\pi )$$

Get the value of \sin(\frac{1}{6}\pi ) from trigonometric values table.

$$2\left(-\frac{1}{2}\right)$$

Multiply 2 and -\frac{1}{2} to get -1.

$$-1$$

Factor

$$-1$$