6.5 Trigonometric Graphs (sine and cosine)

This section was about the trigonometric graphs of sine and cosine.

To start off with, we have the graph of f(x) = sin x:

adding a value in front of sin we can stretch or compress the graph vertically, such as with

f(x) = 2sin x

we call this 'a' in the formula f(x) = a sin (bx-c)+d. b will stretch or compress vertically (although smaller numbers stretch and larger numbers compress), c will transform the graph horizontally (like b, it is counter intuitive), and d will transform vertically. For example, the graph of

f(x) = sin x+5

is shifted 5 up from f(x) = sin x, and f(x) =3 sin (1/3x-3)

is stretched vertically by a factor of 3, stretched horizontally by a factor of 3 and moved 3 to the right.

If a is negative, that will flip the graph over the midline, and if b is negative, that will flip the graph over the y-axis.

You can use the formula to draw the graph by knowing that |a|= amplitude and period = 2π/|b|.

You can also use the amplitude and period to figure out the original values of a and b in the function by taking the measurements of the amplitude and period.

All of these rules apply to cosine, but f(x) = cos x looks like

Thanks for reading, and i apologize for my abysmal post writing skills.

Dan