40. Express

Question

4 cos 𝑥 + 3 sin 𝑥 in the
form Rsin(𝑥 + 𝜃)
A. 5Sin(x+36.9)
B. 5Sin(x+53.1)
C. 7Sin(x+36.9)
D. 7Sin(x+53.1)
X
Y

Answer 1

To express 4 cos 𝑥 + 3 sin 𝑥 in the form Rsin(𝑥 + 𝜃), we first need to find the value of R and 𝜃.

Using the identity cos(𝑎 - 𝑏) = cos 𝑎 cos 𝑏 + sin 𝑎 sin 𝑏, we can rewrite the expression as:

4 cos 𝑥 + 3 sin 𝑥 = 5 cos 𝑥 cos 36.9° + 5 sin 𝑥 sin 36.9°

We can see that this expression is in the form Rsin(𝑥 + 𝜃) with R = 5 and 𝜃 = 36.9°.

Therefore, the answer is (A) 5Sin(x+36.9).