Question

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression.
\\( \sin 5 ^ { \circ } \cos 85 ^ { \circ } + \cos 5 ^ { \circ } \sin 85 ^ { \circ } \\)
write the expression as the sine, cosine, or tangent of an angle.
\\( \sin 5 ^ { \circ } \cos 85 ^ { \circ } + \cos 5 ^ { \circ } \sin 85 ^ { \circ } = \sin 90 ^ { \circ } \\)
(type an exact answer, using ( \pi ) as needed. use integers or fractions for any numbers in the expression.)
find the exact value of the expression.
\\( \sin 5 ^ { \circ } \cos 85 ^ { \circ } + \cos 5 ^ { \circ } \sin 85 ^ { \circ } = \square \\)
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Recall the sine addition formula

The formula for \(\sin(A + B)=\sin A\cos B+\cos A\sin B\). Here \(A = 5^{\circ}\) and \(B=85^{\circ}\), so \(\sin5^{\circ}\cos85^{\circ}+\cos5^{\circ}\sin85^{\circ}=\sin(5^{\circ}+85^{\circ})\).

Step2: Calculate the value of the sine function

Since \(5^{\circ}+85^{\circ}=90^{\circ}\), and we know that \(\sin90^{\circ}=1\).

Answer:

\(1\)