First, let us use the identity π
sin(π₯+π) = π
cos(π)sin(π₯) + π
sin(π)cos(π₯) to rewrite the expression in the desired form.
We can rewrite 4 cos π₯ + 3 sin π₯ as:
4 cos π₯ + 3 sin π₯ = π
cos(π)sin(π₯) + π
sin(π)cos(π₯)
where π
and π are constants that we need to determine.
To find π
and π, we can use the following relationships:
π
= β(4^2 + 3^2) = 5
tan π = 3/4
π β 36.87Β°
Therefore, we have:
4 cos π₯ + 3 sin π₯ = 5 cos(36.87Β°) sin π₯ + 5 sin(36.87Β°) cos π₯
So, the expression in the form Rsin(π₯ + π) is:
5 sin(π₯ + 36.87Β°)
Express
4 cos π₯ + 3 sin π₯ in the
form Rsin(π₯ + π)
1 answer