Solve cospi/3-3sin3pi/2+1/3sinpi/2+cospi

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

Evaluate

$$\frac{17}{6}\approx 2.833333333$$

Solution Steps

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

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

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

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

Multiply 3 and -1 to get -3.

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

The opposite of -3 is 3.

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

Add \frac{1}{2} and 3 to get \frac{7}{2}.

$$\frac{7}{2}+\frac{1}{3}\sin(\frac{\pi }{2})+\cos(\pi )$$

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

$$\frac{7}{2}+\frac{1}{3}\times 1+\cos(\pi )$$

Multiply \frac{1}{3} and 1 to get \frac{1}{3}.

$$\frac{7}{2}+\frac{1}{3}+\cos(\pi )$$

Add \frac{7}{2} and \frac{1}{3} to get \frac{23}{6}.

$$\frac{23}{6}+\cos(\pi )$$

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

$$\frac{23}{6}-1$$

Subtract 1 from \frac{23}{6} to get \frac{17}{6}.

$$\frac{17}{6}$$

Factor

$$\frac{17}{2 \cdot 3} = 2\frac{5}{6} = 2.8333333333333335$$