Solve 6cos45^circ+(1/3)^-1+1+5-3sqrt{2}+(-1)

$$6 \cos 45 ^ { \circ } + ( \frac { 1 } { 3 } ) ^ { - 1 } + 1 + 5 - 3 \sqrt { 2 } + ( - 1 )$$

Evaluate

$$8$$

Solution Steps

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

$$6\times \frac{\sqrt{2}}{2}+\left(\frac{1}{3}\right)^{-1}+1+5-3\sqrt{2}-1$$

Cancel out 2, the greatest common factor in 6 and 2.

$$3\sqrt{2}+\left(\frac{1}{3}\right)^{-1}+1+5-3\sqrt{2}-1$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$3\sqrt{2}+3+1+5-3\sqrt{2}-1$$

Add 3 and 1 to get 4.

$$3\sqrt{2}+4+5-3\sqrt{2}-1$$

Add 4 and 5 to get 9.

$$3\sqrt{2}+9-3\sqrt{2}-1$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$9-1$$

Subtract 1 from 9 to get 8.

$$8$$