Solve 1-11+tan(45^circ)-(sqrt{2})*sin(45^circ)+2^-1

$$1-11+ \tan ( 45 ^ { \circ } ) -( \sqrt{ 2 } ) \times \sin ( 45 ^ { \circ } ) + { 2 }^{ -1 }$$

Evaluate

$$-\frac{19}{2}=-9.5$$

Solution Steps

Subtract 11 from 1 to get -10.

$$-10+\tan(45)-\sqrt{2}\sin(45)+2^{-1}$$

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

$$-10+1-\sqrt{2}\sin(45)+2^{-1}$$

Add -10 and 1 to get -9.

$$-9-\sqrt{2}\sin(45)+2^{-1}$$

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

$$-9-\sqrt{2}\times \frac{\sqrt{2}}{2}+2^{-1}$$

Express \sqrt{2}\times \frac{\sqrt{2}}{2} as a single fraction.

$$-9-\frac{\sqrt{2}\sqrt{2}}{2}+2^{-1}$$

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

$$-9-\frac{2}{2}+2^{-1}$$

Divide 2 by 2 to get 1.

$$-9-1+2^{-1}$$

Subtract 1 from -9 to get -10.

$$-10+2^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$-10+\frac{1}{2}$$

Add -10 and \frac{1}{2} to get -\frac{19}{2}.

$$-\frac{19}{2}$$