Solve sinpi/6+4cospi/3-3cospi-sinpi/4

$$\sin \frac { \pi } { 6 } + 4 \cos \frac { \pi } { 3 } - 3 \cos \pi - \sin \frac { \pi } { 4 }$$

Evaluate

$$\frac{11-\sqrt{2}}{2}\approx 4.792893219$$

Solution Steps

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

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

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

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

Multiply 4 and \frac{1}{2} to get 2.

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

Add \frac{1}{2} and 2 to get \frac{5}{2}.

$$\frac{5}{2}-3\cos(\pi )-\sin(\frac{\pi }{4})$$

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

$$\frac{5}{2}-3\left(-1\right)-\sin(\frac{\pi }{4})$$

Multiply 3 and -1 to get -3.

$$\frac{5}{2}-\left(-3\right)-\sin(\frac{\pi }{4})$$

The opposite of -3 is 3.

$$\frac{5}{2}+3-\sin(\frac{\pi }{4})$$

Add \frac{5}{2} and 3 to get \frac{11}{2}.

$$\frac{11}{2}-\sin(\frac{\pi }{4})$$

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

$$\frac{11}{2}-\frac{\sqrt{2}}{2}$$

Since \frac{11}{2} and \frac{\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{11+\sqrt{2}}{2}$$