What is the equation for a sine function graph with a period of 2 and an amplitude of 2

period = 2, Amplitude = 2

AMPLITUDE

f(t) = sin(t) , this function has an amplitude of 1 , because its y values goes one unit up, and one unit down from the x axis. to increase this to an amplitude of 2, we get f(t) = 2. sin(t). This means the graph is twice as tall as our original function f(t) = 1.sin(t).

PERIOD

the period has a formula: w = 2pi / |B | . The normal period for a sinewave

f(t) = sin(t) = 2 pi.

So in our new function f(t) = 2 sin (t) [ amplitude is now multiplied by 2], the period (as stated in the question) is 2, that is 2 pi (remember the formula for period stated 2pi) divided by b, which is now 2. Which means 2pi is now divided by 2 or multiplied by 1/2. 2pi /2 = pi or 1/2 x 2pi = pi.  so as you increase the period in the equation, the sinewave becomes shorter.

ANSWER

So the function is actually f(t) = 2.sin(2t).

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step-by-step explanation:

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (