For the function y=-3+4 cos(5pi/6(x+4)) , what is the minimum value?
the min of cos (???) = -1
so the min of 4cos ?? = -4
so the min of -3 + 4 cos ?? = -7
Well, to find the minimum value of the function, we need to find the lowest point on the graph. And if we're talking about lows, I can't help but think about my bank account. It's so low, it should come with a ladder. Anyway, back to the question!
To find the minimum value, we need to determine the lowest point on the graph. In this case, the function is in the form of y = A cos(B(x - C)) + D, where A, B, C, and D are constants.
The general formula for the minimum value of a cosine function is D - A, where D is the vertical shift (or the y-intercept) and A is the amplitude. So if we apply this formula to our function, we find that the minimum value is -3 - 4 = -7.
So, to summarize, the minimum value of the function y = -3 + 4 cos(5pi/6(x + 4)) is -7. Just like my bank account! Ha!
To find the minimum value of the function, we need to determine the lowest point on the graph.
First, let's analyze the given function:
y = -3 + 4cos[(5π/6)(x+4)]
The cosine function oscillates between -1 and 1.
Since the coefficient of the cosine function is positive (4), the maximum value of the cosine function will be 4.
The minimum value occurs when the cosine function has its maximum, which is -1.
So, the minimum value of the function is:
-3 + 4(-1)
= -3 - 4
= -7
To find the minimum value of the function y = -3 + 4 cos(5pi/6(x + 4)), we can start by understanding the behavior of the cosine function.
The cosine function oscillates between -1 and 1 with a period of 2pi. It reaches its minimum value of -1 when the angle is (2n + 1)pi, where n is an integer. In this case, we have a cosine function with a period of 2pi/5. So, its minimum value will occur when the angle is (2n + 1)(2pi/5).
Now, let's find the value of x that gives the minimum value for the function y. We set the argument of the cosine function equal to (2n + 1)(2pi/5) and solve for x:
5pi/6(x + 4) = (2n + 1)(2pi/5)
To solve for x, we can start by isolating the variable:
x + 4 = (2n + 1)(2pi/5) * (6/5pi)
Next, simplify the expression:
x + 4 = 12n/5 + 6pi/5 + 12/5
Finally, subtract 4 from both sides to get the value of x:
x = 12n/5 + 6pi/5 + 12/5 - 4
x = 12n/5 + 6pi/5 + 8/5
Now that we have the value of x, we can substitute it back into the original function to find the minimum y-value:
y = -3 + 4 cos(5pi/6(x + 4))
y = -3 + 4 cos(5pi/6((12n/5) + (6pi/5) + (8/5)))
You can substitute different values of n into this equation to find the respective minimum y-values for each value of x.