For the given function, determine the amplitude and find the phase shift.
-y = 15 sin x + 20 cos x Give the phase shift in radians rounded to the nearest thousandth.
A) 35, 0.644
B) 25, 0.927
C) 25, - 0.644
D) 25, - 0.927

Question

Quizplus · Accepted Answer

The amplitude is found using the formula √(a² + b²) for y = a sin x + b cos x, which gives √(15² + 20²) = 25. The phase shift is calculated using arctan(b/a), which gives arctan(20/15) ≈ 0.927 radians. Since the cosine term is positive, the phase shift is negative.

For the Given Function, Determine the Amplitude and Find the Phase