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High School Precalculus: Help and Review32 chapters | 297 lessons

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Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this how-to lesson, you'll learn how you can find the vertical shift of any trig function easily just by looking at one particular number in the whole function.

In this lesson, you'll learn how to find the vertical shift of any trig function. A **trig function** is a function with a trigonometry function in it such as sine, cosine, tangent, or cotangent. For example, *y* = 3 sin (2*x* - 3) + 4 is an example of a trig function. To find the vertical shift of such as function, simply follow these easy steps.

The first thing you need to do is to remember the general form of the trig function.

The A stands for the amplitude of the trig function. The 'trig' word stands for the trig function you have whether it is sine, cosine, tangent, or cotangent. The B helps you calculate the period of the function. If you divide the C by the B (C / B), you'll get your phase shift. The D is your vertical shift. The **vertical shift** of a trig function is the amount by which a trig function is transposed along the *y*-axis, or, in simpler terms, the amount it is shifted up or down.

If the function you are given doesn't look like the one above, you'll need to rewrite it so it does.

For our example, *y* = 3 sin (2*x* - 3) + 4, the function is already in standard form with sine being our trig function. The A is 3, the B is 2, the C is 3, and the D is 4. Note that the C value is positive. This is because in the general form, the C value is being subtracted. This means that if the C value is being added in the general equation form, then the C value is negative.

The next step, and our last step, is to locate the vertical shift as shown in the general form of the trig function. The general form tells you that the vertical shift is given by the value D. All you have to do is to look at that value and it will give you your answer.

Because our D value is 4 for our example, *y* = 3 sin (2*x* - 3) + 4, the vertical shift is 4. And that's all you need to do.

Let's look at another example.

Find the vertical shift of this trig function.

The first step is to remember the general form.

Looking at our problem, we see that it doesn't quite follow the format. So, we'll need to rewrite it so it does. To do this, we'll simply rearrange, so that we are adding the 3 in the end instead of having the 3 in the beginning. This way, our formula matches with the general form and we can easily find what our A, B, C, and D values are.

Next, we locate our D value. Now that we've rewritten our trig function, we see that our D value is 3. And there we have our answer. Our vertical shift is 3 since our D value is 3. And we are done!

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10 in chapter 21 of the course:

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High School Precalculus: Help and Review32 chapters | 297 lessons

- Graphing Sine and Cosine Transformations 8:39
- Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift 9:42
- Graphing the Cosecant, Secant & Cotangent Functions 7:10
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- Solving a Trigonometric Equation Graphically 5:45
- How to Graph cos(x)
- How to Graph 1-cos(x) 6:15
- How to Find the Period of a Trig Function 4:19
- How to Find the Phase Shift of a Trig Function
- How to Find the Vertical Shift of a Trig Function
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