Solve [sqrt{2}*(cospi/4+sinpi/4)]*cos2/3pi*sin2/3pi

$$[ \sqrt { 2 } \cdot ( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } ) ] \cdot \cos \frac { 2 } { 3 } \pi \cdot \sin \frac { 2 } { 3 } \pi$$

Evaluate

$$-0.48123702903881748$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\sqrt{2} \cdot {(\cos(\frac{\pi}{4}) + \sin(\frac{\pi}{4}))})} \cdot -0.24061851451940874$$

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

$$\sqrt{2}\left(\frac{\sqrt{2}}{2}+\sin(\frac{\pi }{4})\right)\left(-0.24061851451940874\right)$$

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

$$\sqrt{2}\left(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\right)\left(-0.24061851451940874\right)$$

Combine \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{2} to get \sqrt{2}.

$$\sqrt{2}\sqrt{2}\left(-0.24061851451940874\right)$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\left(-0.24061851451940874\right)$$

Multiply 2 and -0.24061851451940874 to get -0.48123702903881748.

$$-0.48123702903881748$$

Factor

$$-0.48123702903881748$$