Question

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression.
\\( \sin 40 ^ { \circ } \cos 50 ^ { \circ } + \cos 40 ^ { \circ } \sin 50 ^ { \circ } \\)
write the expression as the sine, cosine, or tangent of an angle.
\\( \sin 40 ^ { \circ } \cos 50 ^ { \circ } + \cos 40 ^ { \circ } \sin 50 ^ { \circ } = \square ^ { \circ } \\)
(type an exact answer, using \\( \pi \\) as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Use the sine addition formula

The formula for \(\sin(A + B)=\sin A\cos B+\cos A\sin B\). Here \(A = 40^{\circ}\) and \(B=50^{\circ}\). So \(\sin40^{\circ}\cos50^{\circ}+\cos40^{\circ}\sin50^{\circ}=\sin(40^{\circ}+ 50^{\circ})\).

Step2: Calculate the sum of angles

\(40^{\circ}+50^{\circ}=90^{\circ}\). And we know that \(\sin90^{\circ}=1\).

Answer:

\(\sin90^{\circ}\), and the exact value is \(1\)