Solve sin40/cos45=

$$\frac { \sin 40 } { \cos 45 } =$$

Evaluate

$$\frac{6427876096865393\sqrt{2}}{10000000000000000}\approx 0.909038955$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.6427876096865393}{\cos(45)}$$

Get the value of \cos(45) from trigonometric values table.

$$\frac{0.6427876096865393}{\frac{\sqrt{2}}{2}}$$

Divide 0.6427876096865393 by \frac{\sqrt{2}}{2} by multiplying 0.6427876096865393 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{0.6427876096865393\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{0.6427876096865393\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{0.6427876096865393\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{0.6427876096865393\times 2\sqrt{2}}{2}$$

Multiply 0.6427876096865393 and 2 to get 1.2855752193730786.

$$\frac{1.2855752193730786\sqrt{2}}{2}$$

Divide 1.2855752193730786\sqrt{2} by 2 to get 0.6427876096865393\sqrt{2}.

$$0.6427876096865393\sqrt{2}$$