Solve sin5^circcos25^circ+cos5^circsin25^circ

$$\sin 5 ^ { \circ } \cos 25 ^ { \circ } + \cos 5 ^ { \circ } \sin 25 ^ { \circ }$$

Evaluate

$$0.499999999999999981413397647637203$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.08715574274765817 \cdot 0.9063077870366499 + 0.9961946980917455 \cdot 0.42261826174069944$$

Multiply 0.08715574274765817 and 0.9063077870366499 to get 0.078989928337165624741297187164683.

$$0.078989928337165624741297187164683+0.9961946980917455\times 0.42261826174069944$$

Multiply 0.9961946980917455 and 0.42261826174069944 to get 0.42101007166283435667210046047252.

$$0.078989928337165624741297187164683+0.42101007166283435667210046047252$$

Add 0.078989928337165624741297187164683 and 0.42101007166283435667210046047252 to get 0.499999999999999981413397647637203.

$$0.499999999999999981413397647637203$$

Factor

$$\frac{3 \cdot 11 \cdot 1499 \cdot 4931 \cdot 94239667 \cdot 21751323433695217}{2 ^ {33} \cdot 5 ^ {33}} = 0.5$$