Solve 4sin(85)cos(55)/5sqrt{91}

$$4 \sin ( 85 ) \frac{ \cos ( 55 ) }{ 5 \sqrt{ 91 } }$$

Evaluate

$$\frac{571393804843269548895352890793\sqrt{91}}{113750000000000000000000000000000}\approx 0.047918677$$

Solution Steps

Evaluate trigonometric functions in the problem

$$4 \cdot 0.9961946980917455 \frac{0.573576436351046}{5 \sqrt{91}}$$

Multiply 0.9961946980917455 and 4 to get 3.984778792366982.

$$3.984778792366982\times \frac{0.573576436351046}{5\sqrt{91}}$$

Rationalize the denominator of \frac{0.573576436351046}{5\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$3.984778792366982\times \frac{0.573576436351046\sqrt{91}}{5\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$3.984778792366982\times \frac{0.573576436351046\sqrt{91}}{5\times 91}$$

Multiply 5 and 91 to get 455.

$$3.984778792366982\times \frac{0.573576436351046\sqrt{91}}{455}$$

Divide 0.573576436351046\sqrt{91} by 455 to get \frac{286788218175523}{227500000000000000}\sqrt{91}.

$$3.984778792366982\times \frac{286788218175523}{227500000000000000}\sqrt{91}$$

Multiply 3.984778792366982 and \frac{286788218175523}{227500000000000000} to get \frac{571393804843269548895352890793}{113750000000000000000000000000000}.

$$\frac{571393804843269548895352890793}{113750000000000000000000000000000}\sqrt{91}$$