Graph each function over a two-period interval.
y = sin ...

Question

Graph each function over a two-period interval.

y = sin (x + π/4)

Accepted Answer

Graph. The following function considering two periods, we have Y equals sine X plus pi divided by three. Now to graph this, let's first look at our general form of sin of X. The general form is Y equals A S B multiplied by X minus C plus D where A is our amplitude period, it is two pi divided by B face shift is C in vertical shift is T. Now we can look at our function and determine these values. You know A is one because there's no number we see period is two pi divided by one or just two pi and our horizontal shift, it's just negative pi divided by three. We can tell this because we have X plus pi divided by three, which in our base function is X minus negative pi divided by three. So we have a horizontal shift of pi divided by three to the left. And finally, we do not have a vertical shift. So we don't have devalue. So our only transformation now is the sine graph and swarmed by moving I divided by three to the left, which means we can take our normal sign function and just move it over. So we draw a little graph here down, you know the sign function it starts at 00 in this period is to cut, I will draw a few points here just so we can see what it looks like. Now, I will also draw a couple other things on other graph here to show that we're transforming and we will do the same thing pie, two pie, three pie and four pie. Now in the S graph making a little table gives us the points zero pi two pie that gives us a zero, zero and zero, which means we had a couple other points. Let's take pi divided by two and three pi divided by two to give us one and negative one. We'll do the same or or other graph meaning our values will stay the same for our wives. She says her exes will be shifted now and the P divided by three, two P divided by three, five pi divided by three. Then we have pi divided by two and three pie divided by two. That is pi divided by six and four pi divided by three. Now we can just plot all of these onto our graphs. 00 pi divided by 21, 503 pi divided by two negative 12 pi since we are doing two periods, we will loop the same points giving us our base sine function. Since we are shifting it over, we will just move everything to the left by pi divided by three. We can now see look something like this. Ok. I hope to help you solve the problem. Thank you for watching. Get back.

Graph each function over a two-period interval.
y = sin (x + π/4)

Key Concepts

Sine Function

Phase Shift

Graphing Trigonometric Functions

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