Solve 2tan2-cos2/2-3sin2

$$2 \tan 2 - \frac { \cos 2 } { 2 } - 3 \sin 2$$

Evaluate

$$-0.53455236463355535$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 0.03492076949174773 - \frac{0.9993908270190958}{2} - 3 \cdot 0.03489949670250097$$

Multiply 2 and 0.03492076949174773 to get 0.06984153898349546.

$$0.06984153898349546-\frac{0.9993908270190958}{2}-3\times 0.03489949670250097$$

Expand \frac{0.9993908270190958}{2} by multiplying both numerator and the denominator by 10000000000000000.

$$0.06984153898349546-\frac{9993908270190958}{20000000000000000}-3\times 0.03489949670250097$$

Reduce the fraction \frac{9993908270190958}{20000000000000000} to lowest terms by extracting and canceling out 2.

$$0.06984153898349546-\frac{4996954135095479}{10000000000000000}-3\times 0.03489949670250097$$

Convert decimal number 0.06984153898349546 to fraction \frac{3492076949174773}{10000000000}. Reduce the fraction \frac{3492076949174773}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{3492076949174773}{50000000000000000}-\frac{4996954135095479}{10000000000000000}-3\times 0.03489949670250097$$

Least common multiple of 50000000000000000 and 10000000000000000 is 50000000000000000. Convert \frac{3492076949174773}{50000000000000000} and \frac{4996954135095479}{10000000000000000} to fractions with denominator 50000000000000000.

$$\frac{3492076949174773}{50000000000000000}-\frac{24984770675477395}{50000000000000000}-3\times 0.03489949670250097$$

Since \frac{3492076949174773}{50000000000000000} and \frac{24984770675477395}{50000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3492076949174773-24984770675477395}{50000000000000000}-3\times 0.03489949670250097$$

Subtract 24984770675477395 from 3492076949174773 to get -21492693726302622.

$$\frac{-21492693726302622}{50000000000000000}-3\times 0.03489949670250097$$

Reduce the fraction \frac{-21492693726302622}{50000000000000000} to lowest terms by extracting and canceling out 2.

$$-\frac{10746346863151311}{25000000000000000}-3\times 0.03489949670250097$$

Multiply 3 and 0.03489949670250097 to get 0.10469849010750291.

$$-\frac{10746346863151311}{25000000000000000}-0.10469849010750291$$

Convert decimal number 0.10469849010750291 to fraction \frac{10469849010750291}{10000000000}. Reduce the fraction \frac{10469849010750291}{10000000000} to lowest terms by extracting and canceling out 1.

$$-\frac{10746346863151311}{25000000000000000}-\frac{10469849010750291}{100000000000000000}$$

Least common multiple of 25000000000000000 and 100000000000000000 is 100000000000000000. Convert -\frac{10746346863151311}{25000000000000000} and \frac{10469849010750291}{100000000000000000} to fractions with denominator 100000000000000000.

$$-\frac{42985387452605244}{100000000000000000}-\frac{10469849010750291}{100000000000000000}$$

Since -\frac{42985387452605244}{100000000000000000} and \frac{10469849010750291}{100000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-42985387452605244-10469849010750291}{100000000000000000}$$

Subtract 10469849010750291 from -42985387452605244 to get -53455236463355535.

$$\frac{-53455236463355535}{100000000000000000}$$

Reduce the fraction \frac{-53455236463355535}{100000000000000000} to lowest terms by extracting and canceling out 5.

$$-\frac{10691047292671107}{20000000000000000}$$

Factor

$$-0.53455236463355535$$