Please help me with this

Question

Find the amplitude and midline.

(20-7sin t)/(10)

Midline: y=

Amplitude=

Answer 1

Standard formula for the sine function is f(x) = (A)sin(B)(x-C)+D where D is the vertical shift (or Midline) and |A| is the amplitude. [Note: 2π/B = Period and C = horizontal shift]

So we need to take the equation and put it into the general format for the sine equation.

(20-7sin(t))/10 = 20/10 - (7/10)sin(t) = -(7/10)sin(t) + 2

So midline = 2 and Amplitude = |-(7/10)| = 0.7

Additionally, here, B = 1 and C = 0, so the period is 2π and the horizontal shift = 0.

Answer 2

midline = 20/10 = 2

amplitude = 7/10 = 0.7