For each function, give the amplitude, period, vertical transl...

Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sin 2x

Accepted Answer

Hello. Today we are going to be finding the amplitude period, vertical translation and phase shift. For the following trigonometric function we are given Y is equal to four sin of four X. So how can we obtain these four pieces of information? Well, in order to get these four pieces of information, we can compare the given trigonometric function to the general function Y is equal to a multiplied by sine of B multiplied by X minus C plus D. Using this function, let's start by identifying the amplitude of our sine function. Now the amplitude is going to equal the absolute value of the ater. This is where the A term is the coefficient in front of the sine function. The coefficient in front of our given sine function is four. That means our amplitude is going to equal to the absolute value of four which will simplify to give us positive four. So the amplitude for a given sine function is going to be four. Now we will identify the period of the function. The period of a sine function is defined as two pi divided by the absolute value of B. This is where B is the coefficient in front of the X minus C term, that coefficient is given to us as four. So our period will equal to two pi divided by the absolute value of four. This will simplify to leave us with two pi divided by four and will further simplify to be pi divided by two. So the final period of our sine function is equal to pi divided by two. Now, what we are going to do is we are going to identify any phase shift of the function. Now, the phase shift can be thought of as a horizontal shift of the function. And the phase shift is defined as the C term of the function. Now, if we take a look at our given function, we are not given ac term. What this means is that our phase shift is going to equal to zero. And this means that we have no face shift. Finally, we are going to identify a vertical shift of the function. The vertical shift is the D term and this is where the D term is any amount that we are adding or subtracting to the sine function. Well, we are not adding or subtracting any values to the sine function. So we can represent the D term by adding zero to our sine function. That means we have a vertical shift of zero, meaning that there is no vertical shift. So there are only two pieces of information that we obtained from the function we have an amplitude of four and we have a period of pi divided by two. With that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 2x

Key Concepts

Amplitude of a Sine Function

Period of a Sine Function

Vertical Translation and Phase Shift

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