Graphing sine curve, where do you start on the graph?

Question

Do you start from 0 or from the amplitude? Amplitude can never be negative because it is an absolute value right? |a|

So when I graph a sine equation.. say y = -sin(2x)

do I start the curve off at 1 (|a|), 0 or -1 (a)? What about cos? Cos starts at amplitude so it always starts positive?

Answer 1

sin(0) = 0, so start at 0. y = -sin(2x) starts at 0 and heads negative as x moves in the positive direction from zero.

With cos, it depends on the equation. cos(0) = 1, but if there is a negative coefficient, you'd start at the negative value:

y = -3 cos(x)

... starts at -3 when x=0 and moves upward as x increases from zero.

Answer 2

On a sine graph without vertical or horizontal shift, when x = 0, then f(x) (function of x) is zero as well. On the graph y = -sin(2x), when x = 0, y = 0, since sin(2*0) = 0, and negative 0 is 0 anyways.
On a cosine graph, like y = cos(x), when x = 0, y = 1, since cosine of zero is always one. However, if you have something like y = 3cos(x) and you plug in zero (or 2pi) for x, then y = 3 (which is the amplitude of the equation).
If you would like any more math help, I am usually available.
Hope this helps!

Answer 3

The Sine Curve

Answer 4

you're top appropriate to the amplitude. appropriate to the era, you're top too. Now, the (x - pi) could supply you a small venture in case you haven't any longer learnt that yet. while (x - pi) is secure in such an equation, it ability the line is moved top via pi gadgets. so which you relatively already have the graph, purely flow it pi gadgets over and you gets it top. :) So, the graph could have the final ingredient of a sine function ranging in y from -a million/2 to a million/2 as a results of amplitude. The graph is purely shifted over.

Answer 5

any place...it is infinite in each direction...