Solve 18-(pi-1)^0-2cos45^circ+(1/4)^-1

$$18 - ( \pi - 1 ) ^ { 0 } - 2 \cos 45 ^ { \circ } + ( \frac { 1 } { 4 } ) ^ { - 1 }$$

Evaluate

$$21-\sqrt{2}\approx 19.585786438$$

Solution Steps

Calculate \pi -1 to the power of 0 and get 1.

$$18-1-2\cos(45)+\left(\frac{1}{4}\right)^{-1}$$

Subtract 1 from 18 to get 17.

$$17-2\cos(45)+\left(\frac{1}{4}\right)^{-1}$$

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

$$17-2\times \frac{\sqrt{2}}{2}+\left(\frac{1}{4}\right)^{-1}$$

Cancel out 2 and 2.

$$17-\sqrt{2}+\left(\frac{1}{4}\right)^{-1}$$

Calculate \frac{1}{4} to the power of -1 and get 4.

$$17-\sqrt{2}+4$$

Add 17 and 4 to get 21.

$$21-\sqrt{2}$$