Find the amplitude, period, phase shift, and vertical displacement for:
y=7sin5(x-85degrees)-1.2
just read 'em off the function
amplitude 7
period 2pi
shift 85 degrees
displ -1.2
what about the phase shift in radians?
To find the amplitude, period, phase shift, and vertical displacement for the given equation y = 7sin(5(x - 85°)) - 1.2, we need to understand the general form of a trigonometric equation.
The general form of a trigonometric equation is y = A*sin(B(x - C)) + D, where:
A = amplitude
B = 2π/period
C = phase shift
D = vertical displacement
Let's break down the given equation to match the general form.
The equation y = 7sin(5(x - 85°)) - 1.2 can be rewritten as follows:
A = 7
B = 5
C = 85°
D = -1.2
Amplitude:
The amplitude, A, is the absolute value of the coefficient multiplied by the function or trigonometric term. In this case, the amplitude is 7.
Period:
The period, P, is calculated using the formula P = 2π/B. Here, B is 5, so the period is P = 2π/5.
Phase Shift:
The phase shift, C, is derived from the expression (x - C). In this equation, C is given as 85°. To convert it into radians, multiply by π/180: C = 85° * π/180.
Vertical Displacement:
The vertical displacement, D, is the constant term added or subtracted in the equation. Here, D is -1.2.
By evaluating the given equation, we have:
Amplitude = 7
Period = 2π/5
Phase Shift = 85° * π/180
Vertical Displacement = -1.2
Therefore, the answers for the given equation are:
Amplitude = 7
Period ≈ 1.256
Phase Shift ≈ 1.483
Vertical Displacement = -1.2