How to Find the Vertical Shift of a Trig Function

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.

The Steps

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 (2x - 3) + 4 is an example of a trig function. To find the vertical shift of such as function, simply follow these easy steps.

Step 1: Remember the general form of a trig function.

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

vertical shift

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 (2x - 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.

Step 2: Locate the vertical shift.

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.

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