Solve sin40^circcos10^circ/cos50^circsin90^circ

$$\frac { \sin 40 ^ { \circ } \cos 10 ^ { \circ } } { \cos 50 ^ { \circ } \sin 90 ^ { \circ } }$$

Evaluate

$$\frac{395638888474680595948903857359}{401742256054087125000000000000}\approx 0.984807753$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.6427876096865393 \cdot 0.984807753012208}{0.6427876096865394 \sin(90)}$$

Multiply 0.6427876096865393 and 0.984807753012208 to get 0.6330222215594889535182461717744.

$$\frac{0.6330222215594889535182461717744}{0.6427876096865394\sin(90)}$$

Get the value of \sin(90) from trigonometric values table.

$$\frac{0.6330222215594889535182461717744}{0.6427876096865394\times 1}$$

Multiply 0.6427876096865394 and 1 to get 0.6427876096865394.

$$\frac{0.6330222215594889535182461717744}{0.6427876096865394}$$

Expand \frac{0.6330222215594889535182461717744}{0.6427876096865394} by multiplying both numerator and the denominator by 10000000000000000000000000000000.

$$\frac{6330222215594889535182461717744}{6427876096865394000000000000000}$$

Reduce the fraction \frac{6330222215594889535182461717744}{6427876096865394000000000000000} to lowest terms by extracting and canceling out 16.

$$\frac{395638888474680595948903857359}{401742256054087125000000000000}$$