What is the equation of the cosine function described?
f(x)=___cos( ___x)
Reiny
answered
The amplitude of the function is 9, the vertical shift is 11 units down, and the period of the function is 12π/7
y = 9cos(7x/6) - 11
Step-by-Step Bot
answered
The standard form of a cosine function is:
f(x) = A*cos(Bx + C) + D
Where:
A represents the amplitude,
B represents the coefficient of x (which controls the period),
C represents the phase shift,
D represents the vertical shift.
In this case:
Amplitude (A) = 9
Vertical shift (D) = 11 (11 units down)
Period = 12π/7
No phase shift is mentioned.
From the given information, we can substitute these values into the standard form equation:
f(x) = 9*cos(Bx) + 11
Now, we need to determine the value of B to represent the period. The period (P) is related to B as follows:
P = 2π / |B|
Given that the period is 12π/7, we can solve for B:
12π/7 = 2π / |B|
Multiplying both sides by |B| and simplifying:
12π = 14π / |B|
14π = 12π / |B|
14π * |B| = 12π
Canceling out the π on both sides:
14 * |B| = 12
|B| = 12 / 14
|B| = 6 / 7
Since no phase shift is mentioned, the value of C in our equation will be 0.
Now we have all the pieces to construct the full equation:
f(x) = 9*cos((6/7)*x) + 11
Therefore, the equation of the cosine function described is:
f(x) = 9*cos((6/7)*x) + 11
Explain Bot
answered
f(x) = A * cos(Bx + C) + D
Where:
A is the amplitude
B determines the period
C is the phase shift
D is the vertical shift
Given that the amplitude is 9 and the vertical shift is 11 units down, we have A = 9 and D = -11.
The period of the function is given as 12π/7, but since there is no phase shift mentioned, we have B = 2π / (period) = 2π / (12π/7) = 7/6.
Plugging these values into the equation, we have:
f(x) = 9 * cos((7/6)x + C) - 11
Since there is no phase shift mentioned, C can be 0.
Therefore, the equation of the cosine function is:
f(x) = 9 * cos((7/6)x) - 11
