Solve 160^circ+4cos90^circ-frac{sqrt{2}}{3}cos45^circ-2cos60^circ-7/2

$$160 ^ { \circ } + 4 \cos 90 ^ { \circ } - \frac { \sqrt { 2 } } { 3 } \cos 45 ^ { \circ } - 2 \cos 60 ^ { \circ } - \frac { 7 } { 2 }$$

Evaluate

$$\frac{931}{6}\approx 155.166666667$$

Solution Steps

Get the value of \cos(90) from trigonometric values table.

$$160+4\times 0-\frac{\sqrt{2}}{3}\cos(45)-2\cos(60)-\frac{7}{2}$$

Multiply 4 and 0 to get 0.

$$160+0-\frac{\sqrt{2}}{3}\cos(45)-2\cos(60)-\frac{7}{2}$$

Add 160 and 0 to get 160.

$$160-\frac{\sqrt{2}}{3}\cos(45)-2\cos(60)-\frac{7}{2}$$

Get the value of \cos(45) from trigonometric values table.

$$160-\frac{\sqrt{2}}{3}\times \frac{\sqrt{2}}{2}-2\cos(60)-\frac{7}{2}$$

Multiply \frac{\sqrt{2}}{3} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$160-\frac{\sqrt{2}\sqrt{2}}{3\times 2}-2\cos(60)-\frac{7}{2}$$

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

$$160-\frac{2}{3\times 2}-2\cos(60)-\frac{7}{2}$$

Multiply 3 and 2 to get 6.

$$160-\frac{2}{6}-2\cos(60)-\frac{7}{2}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$160-\frac{1}{3}-2\cos(60)-\frac{7}{2}$$

Subtract \frac{1}{3} from 160 to get \frac{479}{3}.

$$\frac{479}{3}-2\cos(60)-\frac{7}{2}$$

Get the value of \cos(60) from trigonometric values table.

$$\frac{479}{3}-2\times \frac{1}{2}-\frac{7}{2}$$

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

$$\frac{479}{3}-1-\frac{7}{2}$$

Subtract 1 from \frac{479}{3} to get \frac{476}{3}.

$$\frac{476}{3}-\frac{7}{2}$$

Subtract \frac{7}{2} from \frac{476}{3} to get \frac{931}{6}.

$$\frac{931}{6}$$