Question

Describe the graph of the sine function. Be as specific as possible, including all the properties we studied in this section.

Answer 1

@KamiBug

Answer 2

fan and medal for helper

Answer 3

@kamibug xD

Answer 4

The curve you mean? Like this?

Answer 5

im not sure whatever the question asks

Answer 6

@KamiBug

Answer 7

Well, if it's the case I'm assuming, here are some notes about it. :P
It starts at (0, 0) and has x-intercepts at x = 0, π, 2π, 3π, 4π, etc. This is because of the unit circle. The x-intercepts repeat every π units because that is how far apart the points are that have an x-value of zero. Remember, the sine function is repetitive or periodic because the coordinates start to repeat every 2π revolutions around the unit circle.
It has a maximum point at (pi/2, 1) and a minimum point at (3pi/2, -1).

Answer 8

And this is the standard form of the equation of the function:
f(x) = a sin(bx – c) + d

Answer 9

The value of |a| is the amplitude of the curve and determines the vertical stretching or compressing of the curve.

The value of b determines the period of the graph and determines the horizontal stretching or compressing of the curve. For positive values of b, values less than 1 stretch the period beyond 2π, and values greater than 1 compress the period to less than 2π.
Period = 2pi/|b|

The value of c determines a horizontal shift of the curve along the x-axis. The length of the shift is determined by c/b, also known as the phase shift.
The endpoints of one interval, or cycle, can be determined by solving the equations bx – c = 0 and bx – c = 2π

The value of d is the vertical shift of the trigonometric function along the y-axis. This shift creates a new, imaginary x-axis for the graph to be centered around. It is called the midline.

Answer 10

can you sum all that up?

Answer 11

@KamiBug

Answer 12

could you sum up what you wrote

Answer 13

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