# Write a sine function equation

And we can see that right over here. We can transform and translate trig functions, just like you transformed and translated other functions in algebra. The factorization is: Then the phase shift is. You increase your angle by 2 pi radians or decrease it.

## Writing sine and cosine equations from graphs worksheet

Affiliate Technically, the amplitude is the absolute value of whatever is multiplied on the trig function. So you're going to get to the same point k times faster. So this is y is equal to negative 2. This number is subtracted from the variable, so the shift will be to the right. In your class, use whatever your book or instructor uses. Plugging into the period formula, I get. This is 1. But its midline and its amplitude are not just the plain vanilla sine or cosine function. And we get k is equal to-- let's see.

This would have given me the same value, but more quickly and with less chance of error in the factorization. For this function, the value of the amplitude multiplier A is —2, so the amplitude is: Divided by 2 is negative 2.

### Writing sine and cosine equations from graphs pdf

Multiply both sides by 2pi. This relationship is always true: If a number D is added outside the function, then the graph is shifted up by that number of units; if a number D is subtracted, then the graph is shifted down by that number of units. This is going to have a form something like f of x is equal to the amplitude 3. Affiliate Technically, the amplitude is the absolute value of whatever is multiplied on the trig function. Well, let's just think about the behavior of this function when x is equal to 0. What is the phase shift of? Well, now, your x, your input is increasing k times faster. Find the amplitude, period, phase shift, and vertical shift of The amplitude is given by the multipler on the trig function. If we're at the midline, that means that all of this stuff right over here evaluated to 0. So we can rule out this one right over there.

And so we have this clearly periodic function. This number is subtracted from the variable, so the shift will be to the right.

Graphs of trig functions Video transcript Write the equation of the function f of x graphed below. And we just really need to figure out-- what could this constant actually be?

So immediately you might say, well, this is either going to be a sine function or a cosine function. Whether you're talking about degrees or radians, cosine of 0 is 1.

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