Solve 0.4-9*0.4^2-sin(0.4)-1/18*0.4-cos(0.4)

$$0.4- \frac{ 9 \times { 0.4 }^{ 2 } - \sin ( 0.4 ) -1 }{ 18 \times 0.4- \cos ( 0.4 ) }$$

Evaluate

$$\frac{818796403206321469}{2480009747717842120}\approx 0.330158542$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.4 - \frac{9 \cdot {(0.4)} ^ {2} - 0.0069812602979615525 - 1}{18 \cdot 0.4 - 0.9999756307053947}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$0.4-\frac{9\times 0.16-0.0069812602979615525-1}{18\times 0.4-0.9999756307053947}$$

Multiply 9 and 0.16 to get 1.44.

$$0.4-\frac{1.44-0.0069812602979615525-1}{18\times 0.4-0.9999756307053947}$$

Subtract 0.0069812602979615525 from 1.44 to get 1.4330187397020384475.

$$0.4-\frac{1.4330187397020384475-1}{18\times 0.4-0.9999756307053947}$$

Subtract 1 from 1.4330187397020384475 to get 0.4330187397020384475.

$$0.4-\frac{0.4330187397020384475}{18\times 0.4-0.9999756307053947}$$

Multiply 18 and 0.4 to get 7.2.

$$0.4-\frac{0.4330187397020384475}{7.2-0.9999756307053947}$$

Subtract 0.9999756307053947 from 7.2 to get 6.2000243692946053.

$$0.4-\frac{0.4330187397020384475}{6.2000243692946053}$$

Expand \frac{0.4330187397020384475}{6.2000243692946053} by multiplying both numerator and the denominator by 10000000000000000000.

$$0.4-\frac{4330187397020384475}{62000243692946053000}$$

Reduce the fraction \frac{4330187397020384475}{62000243692946053000} to lowest terms by extracting and canceling out 25.

$$0.4-\frac{173207495880815379}{2480009747717842120}$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}-\frac{173207495880815379}{2480009747717842120}$$

Least common multiple of 5 and 2480009747717842120 is 2480009747717842120. Convert \frac{2}{5} and \frac{173207495880815379}{2480009747717842120} to fractions with denominator 2480009747717842120.

$$\frac{992003899087136848}{2480009747717842120}-\frac{173207495880815379}{2480009747717842120}$$

Since \frac{992003899087136848}{2480009747717842120} and \frac{173207495880815379}{2480009747717842120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{992003899087136848-173207495880815379}{2480009747717842120}$$

Subtract 173207495880815379 from 992003899087136848 to get 818796403206321469.

$$\frac{818796403206321469}{2480009747717842120}$$

Factor

$$\frac{79 \cdot 28697 \cdot 361170555563}{5 \cdot 11 \cdot 5636385790267823 \cdot 2 ^ {3}} = 0.33015854230403546$$