Question

Please help! Somehow not getting the right answer (I checked through the graphs and they’re different)

Answer 1

see explanation

Explanation:

3 cosx - 4 sinx = rcos(x + α) = rcosxcosα - rsinxsinα

Compare like terms on both sides

3 = rcosα and 4 = rsinα

r =
`√(3^2+4^2)` =
`√(9+16)` =
`√(25)` = 5

tanα =
`(sin\alpha )/(cos\alpha )` =
`(4)/(3)` and in first quadrant, thus

α =
`tan^(-1)`(
`(4)/(3)`) ≈ 53.13°

Hence

3cosx - 4sinx = 5cos(x + 53.13)°