Solve cos31^circcos1^circ+sin149^circsin1^circ

$$\cos 31 ^ { \circ } \cos 1 ^ { \circ } + \sin 149 ^ { \circ } \sin 1 ^ { \circ }$$

Evaluate

$$0.866025403784438713311640677665934$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.8571673007021123 \cdot 0.9998476951563913 + 0.5150380749100544 \cdot 0.01745240643728351$$

Multiply 0.8571673007021123 and 0.9998476951563913 to get 0.85703674997043237326044275534299.

$$0.85703674997043237326044275534299+0.5150380749100544\times 0.01745240643728351$$

Multiply 0.5150380749100544 and 0.01745240643728351 to get 0.008988653814006340051197922322944.

$$0.85703674997043237326044275534299+0.008988653814006340051197922322944$$

Add 0.85703674997043237326044275534299 and 0.008988653814006340051197922322944 to get 0.866025403784438713311640677665934.

$$0.866025403784438713311640677665934$$

Factor

$$\frac{3 \cdot 19211 \cdot 249248022251 \cdot 30143778395992949}{2 ^ {32} \cdot 5 ^ {33}} = 0.8660254037844388$$