Question

Consider the following trigonometric function:
g(x)=−sin(8x−3)+5.
What is the midline equation of the function? Give an exact expression.

Answer 1

Definition of Midline

The midline is a horizontal axis that is used as the reference line about which the graph of a periodic function oscillates.

Read more here;

http://www.icoachmath.com/math_dictionary/midline.html

@ http://www.icoachmath.com/math_dictionary/midline.html

Answer 2

@Volkoner If you are live in this thread now, we can do this problem now.

Answer 3

The equation of the midline of periodic function is the average of the maximum and minimum values of the function.

Answer 4

Ok I will try to figure it out from the information you gave me

Answer 5

So i understand the formula needed but i'm not sure how to get the numbers for parts of the formula

Answer 6

@directrix the max is 5? I'm not sure what the amplitude is. 8?

Answer 7

The amplitude is the absolute value of (-1)

−sin(8x−3)+5.

Answer 8

Follow this:

The equation of the midline of periodic function is the average of the maximum and minimum values of the function.

Answer 9

What is the maximum value of sine of x?

What is the minimum value of sine of x?

Post those two and with a little more work, you'll have the midline equation.

Answer 10

Take a look at your graph.

Answer 11

Thank you, I did 6+4 then divided that by 2 to get my answer. y=5

Answer 12

I don't understand how you got the max and min though.

Answer 13

You could look on the graph but that is not necessary if you know that the maximum that sine of an angle can be in its life is 1 and the least that sine of an angle can ever be in its life is -1.

Look at −sin(8x−3)+5 as Negative [ sine (angle)] + 5.

Max value of Negative [ sine (angle)] + 5 will be Negative* (-1) + 5 = 6

Min value of Negative [ sine (angle)] + 5 will be Negative * (1) + 5 = -1 + 5 = 4.