Solve sin127^circcos82^circ-cos127^circsin82^circ

$$\sin 127 ^ { \circ } \cos 82 ^ { \circ } - \cos 127 ^ { \circ } \sin 82 ^ { \circ }$$

Evaluate

$$0.70710678118654781823864377673291$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.7986355100472927 \cdot 0.1391731009600657 - -0.6018150231520484 \cdot 0.9902680687415703$$

Multiply 0.7986355100472927 and 0.1391731009600657 to get 0.11114858047010543166478109913039.

$$0.11114858047010543166478109913039-\left(-0.6018150231520484\times 0.9902680687415703\right)$$

Multiply -0.6018150231520484 and 0.9902680687415703 to get -0.59595820071644238657386267760252.

$$0.11114858047010543166478109913039-\left(-0.59595820071644238657386267760252\right)$$

The opposite of -0.59595820071644238657386267760252 is 0.59595820071644238657386267760252.

$$0.11114858047010543166478109913039+0.59595820071644238657386267760252$$

Add 0.11114858047010543166478109913039 and 0.59595820071644238657386267760252 to get 0.70710678118654781823864377673291.

$$0.70710678118654781823864377673291$$

Factor

$$\frac{11 \cdot 6814133 \cdot 104818804376992036552373 \cdot 3 ^ {2}}{2 ^ {32} \cdot 5 ^ {32}} = 0.7071067811865477$$