Solve sin38^circcos7^circ+sin7^circcos38^circ

$$\sin 38 ^ { \circ } \cos 7 ^ { \circ } + \sin 7 ^ { \circ } \cos 38 ^ { \circ }$$

Evaluate

$$0.70710678118654742819070029750096$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.6156614753256582 \cdot 0.992546151641322 + 0.12186934340514748 \cdot 0.788010753606722$$

Multiply 0.6156614753256582 and 0.992546151641322 to get 0.6110724280483007666303899681404.

$$0.6110724280483007666303899681404+0.12186934340514748\times 0.788010753606722$$

Multiply 0.12186934340514748 and 0.788010753606722 to get 0.09603435313824666156031032936056.

$$0.6110724280483007666303899681404+0.09603435313824666156031032936056$$

Add 0.6110724280483007666303899681404 and 0.09603435313824666156031032936056 to get 0.70710678118654742819070029750096.

$$0.70710678118654742819070029750096$$

Factor

$$\frac{11 \cdot 37 \cdot 269 \cdot 1993 \cdot 2333 \cdot 4663 \cdot 152189 \cdot 12233412329}{2 ^ {28} \cdot 5 ^ {32}} = 0.7071067811865474$$