Solve cospi/3*(cospi/4+sinpi/4)-4cospi/6sinfrac{pi}{3}

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

Evaluate

$$-2.91028543821780157$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.08971456178219843 - 4 \cos(\frac{\pi}{6}) \sin(\frac{\pi}{3})$$

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

$$0.08971456178219843-4\times \frac{\sqrt{3}}{2}\sin(\frac{\pi }{3})$$

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

$$0.08971456178219843-4\times \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

$$0.08971456178219843-4\times \left(\frac{\sqrt{3}}{2}\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$0.08971456178219843-4\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Express 4\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$0.08971456178219843-\frac{4\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$0.08971456178219843-\frac{4\times 3}{2^{2}}$$

Multiply 4 and 3 to get 12.

$$0.08971456178219843-\frac{12}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$0.08971456178219843-\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$0.08971456178219843-3$$

Subtract 3 from 0.08971456178219843 to get -2.91028543821780157.

$$-2.91028543821780157$$

Factor

$$-2.91028543821780157$$