Solve 3/4-cos40^circ+sin10^circ-cos20^circ/2

$$\frac { 3 } { 4 } - \frac { \cos 40 ^ { \circ } + \sin 10 ^ { \circ } - \cos 20 ^ { \circ } } { 2 }$$

Evaluate

$$0.750000000000000035$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3}{4} - \frac{0.766044443118978 + 0.17364817766693033 - 0.9396926207859084}{2}$$

Add 0.766044443118978 and 0.17364817766693033 to get 0.93969262078590833.

$$\frac{3}{4}-\frac{0.93969262078590833-0.9396926207859084}{2}$$

Subtract 0.9396926207859084 from 0.93969262078590833 to get -0.00000000000000007.

$$\frac{3}{4}-\frac{-0.00000000000000007}{2}$$

Expand \frac{-0.00000000000000007}{2} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{3}{4}-\frac{-7}{200000000000000000}$$

Fraction \frac{-7}{200000000000000000} can be rewritten as -\frac{7}{200000000000000000} by extracting the negative sign.

$$\frac{3}{4}-\left(-\frac{7}{200000000000000000}\right)$$

The opposite of -\frac{7}{200000000000000000} is \frac{7}{200000000000000000}.

$$\frac{3}{4}+\frac{7}{200000000000000000}$$

Least common multiple of 4 and 200000000000000000 is 200000000000000000. Convert \frac{3}{4} and \frac{7}{200000000000000000} to fractions with denominator 200000000000000000.

$$\frac{150000000000000000}{200000000000000000}+\frac{7}{200000000000000000}$$

Since \frac{150000000000000000}{200000000000000000} and \frac{7}{200000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{150000000000000000+7}{200000000000000000}$$

Add 150000000000000000 and 7 to get 150000000000000007.

$$\frac{150000000000000007}{200000000000000000}$$

Factor

$$\frac{11 \cdot 13 \cdot 1048951048951049}{2 ^ {18} \cdot 5 ^ {17}} = 0.75$$