Solve 5sin(20)sin(25)sin(35)/3cos(70)cos(65)cos(55)

$$\frac { 5 \sin ( 20 ) \sin ( 25 ) \sin ( 35 ) } { 3 \cos ( 70 ) \cos ( 65 ) \cos ( 55 ) }$$

Evaluate

$$\frac{17101007166283435}{10260604299770064}\approx 1.666666667$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot 0.3420201433256687 \cdot 0.42261826174069944 \cdot 0.573576436351046}{3 \cdot 0.3420201433256688 \cdot 0.42261826174069944 \cdot 0.573576436351046}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{0.3420201433256687\times 5}{0.3420201433256688\times 3\times 0.42261826174069944^{0}\times 0.573576436351046^{0}}$$

Multiply 0.3420201433256687 and 5 to get 1.7101007166283435.

$$\frac{1.7101007166283435}{0.3420201433256688\times 3\times 0.42261826174069944^{0}\times 0.573576436351046^{0}}$$

Multiply 0.3420201433256688 and 3 to get 1.0260604299770064.

$$\frac{1.7101007166283435}{1.0260604299770064\times 0.42261826174069944^{0}\times 0.573576436351046^{0}}$$

Calculate 0.42261826174069944 to the power of 0 and get 1.

$$\frac{1.7101007166283435}{1.0260604299770064\times 1\times 0.573576436351046^{0}}$$

Multiply 1.0260604299770064 and 1 to get 1.0260604299770064.

$$\frac{1.7101007166283435}{1.0260604299770064\times 0.573576436351046^{0}}$$

Calculate 0.573576436351046 to the power of 0 and get 1.

$$\frac{1.7101007166283435}{1.0260604299770064\times 1}$$

Multiply 1.0260604299770064 and 1 to get 1.0260604299770064.

$$\frac{1.7101007166283435}{1.0260604299770064}$$

Expand \frac{1.7101007166283435}{1.0260604299770064} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{17101007166283435}{10260604299770064}$$

Factor

$$\frac{5 \cdot 179 \cdot 25693 \cdot 743676121}{19 \cdot 317 \cdot 11830349747 \cdot 2 ^ {4} \cdot 3 ^ {2}} = 1\frac{6840402866513372}{10260604299770064} = 1.6666666666666663$$