Solve (1/2-a)+3sin^2(pi/4-4)-2

$$( \frac { 1 } { 2 } - a ) + 3 \sin ^ { 2 } ( \frac { \pi } { 4 } - 4 ) - 2$$

Evaluate

$$-a-1.4840373699350726541340492310098125$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{1}{2} - a)} + 3 \cdot 0.07294433965914775 ^ {2} - 2$$

Calculate 0.07294433965914775 to the power of 2 and get 0.0053208766883091152886502563300625.

$$\frac{1}{2}-a+3\times 0.0053208766883091152886502563300625-2$$

Multiply 3 and 0.0053208766883091152886502563300625 to get 0.0159626300649273458659507689901875.

$$\frac{1}{2}-a+0.0159626300649273458659507689901875-2$$

Convert decimal number 0.0159626300649273458659507689901875 to fraction \frac{255402081038837533855212303843}{10000000000}. Reduce the fraction \frac{255402081038837533855212303843}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1}{2}-a+\frac{255402081038837533855212303843}{16000000000000000000000000000000}-2$$

Least common multiple of 2 and 16000000000000000000000000000000 is 16000000000000000000000000000000. Convert \frac{1}{2} and \frac{255402081038837533855212303843}{16000000000000000000000000000000} to fractions with denominator 16000000000000000000000000000000.

$$\frac{8000000000000000000000000000000}{16000000000000000000000000000000}-a+\frac{255402081038837533855212303843}{16000000000000000000000000000000}-2$$

Since \frac{8000000000000000000000000000000}{16000000000000000000000000000000} and \frac{255402081038837533855212303843}{16000000000000000000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{8000000000000000000000000000000+255402081038837533855212303843}{16000000000000000000000000000000}-a-2$$

Add 8000000000000000000000000000000 and 255402081038837533855212303843 to get 8255402081038837533855212303843.

$$\frac{8255402081038837533855212303843}{16000000000000000000000000000000}-a-2$$

Convert 2 to fraction \frac{32000000000000000000000000000000}{16000000000000000000000000000000}.

$$\frac{8255402081038837533855212303843}{16000000000000000000000000000000}-a-\frac{32000000000000000000000000000000}{16000000000000000000000000000000}$$

Since \frac{8255402081038837533855212303843}{16000000000000000000000000000000} and \frac{32000000000000000000000000000000}{16000000000000000000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8255402081038837533855212303843-32000000000000000000000000000000}{16000000000000000000000000000000}-a$$

Subtract 32000000000000000000000000000000 from 8255402081038837533855212303843 to get -23744597918961162466144787696157.

$$-\frac{23744597918961162466144787696157}{16000000000000000000000000000000}-a$$

Factor

$$\frac{-16000000000000000000000000000000a-23744597918961162466144787696157}{16000000000000000000000000000000}$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{1}{2} - a)} + 3 \cdot 0.07294433965914775 ^ {2} - 2$$

Calculate 0.07294433965914775 to the power of 2 and get 0.0053208766883091152886502563300625.

$$factor(\frac{1}{2}-a+3\times 0.0053208766883091152886502563300625-2)$$

Multiply 3 and 0.0053208766883091152886502563300625 to get 0.0159626300649273458659507689901875.

$$factor(\frac{1}{2}-a+0.0159626300649273458659507689901875-2)$$

Convert decimal number 0.0159626300649273458659507689901875 to fraction \frac{255402081038837533855212303843}{10000000000}. Reduce the fraction \frac{255402081038837533855212303843}{10000000000} to lowest terms by extracting and canceling out 1.

$$factor(\frac{1}{2}-a+\frac{255402081038837533855212303843}{16000000000000000000000000000000}-2)$$

Least common multiple of 2 and 16000000000000000000000000000000 is 16000000000000000000000000000000. Convert \frac{1}{2} and \frac{255402081038837533855212303843}{16000000000000000000000000000000} to fractions with denominator 16000000000000000000000000000000.

$$factor(\frac{8000000000000000000000000000000}{16000000000000000000000000000000}-a+\frac{255402081038837533855212303843}{16000000000000000000000000000000}-2)$$

Since \frac{8000000000000000000000000000000}{16000000000000000000000000000000} and \frac{255402081038837533855212303843}{16000000000000000000000000000000} have the same denominator, add them by adding their numerators.

$$factor(\frac{8000000000000000000000000000000+255402081038837533855212303843}{16000000000000000000000000000000}-a-2)$$

Add 8000000000000000000000000000000 and 255402081038837533855212303843 to get 8255402081038837533855212303843.

$$factor(\frac{8255402081038837533855212303843}{16000000000000000000000000000000}-a-2)$$

Convert 2 to fraction \frac{32000000000000000000000000000000}{16000000000000000000000000000000}.

$$factor(\frac{8255402081038837533855212303843}{16000000000000000000000000000000}-a-\frac{32000000000000000000000000000000}{16000000000000000000000000000000})$$

Since \frac{8255402081038837533855212303843}{16000000000000000000000000000000} and \frac{32000000000000000000000000000000}{16000000000000000000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{8255402081038837533855212303843-32000000000000000000000000000000}{16000000000000000000000000000000}-a)$$

Subtract 32000000000000000000000000000000 from 8255402081038837533855212303843 to get -23744597918961162466144787696157.

$$factor(-\frac{23744597918961162466144787696157}{16000000000000000000000000000000}-a)$$

Factor out \frac{1}{16000000000000000000000000000000}.

$$\frac{-23744597918961162466144787696157-16000000000000000000000000000000a}{16000000000000000000000000000000}$$