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Inverse Tangent: Function & Formula

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  • 0:00 Trigonometric Functions
  • 1:04 Inverse Functions
  • 1:42 Inverse Tangent
  • 2:08 Examples
  • 3:35 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

The inverse tangent is the inverse function of the tangent function and can be used to calculate angle measures when certain other things are known. This lesson will go into detail about the inverse tangent, give some formulas, and follow up with a quiz to check your understanding.

Trigonometric Functions

The three most common trigonometric functions are the sine, cosine, and tangent functions.

These functions are all based on a right triangle. They relate the measure of one of the other two angles to a ratio of two of the sides of the triangle.

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Sine = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent = opposite/adjacent

This way, if you know the side measures of a right triangle, you can determine the angle measure by using either the sine, cosine, or tangent functions.

For example - Find the tangent of the given angle, (Θ), which = 30°.

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Since tangent = opposite/adjacent, we can substitute the numbers we know into that equation to find the tangent of the angle.

Tan30° = 4/7 = 0.57

Inverse Functions

All mathematical functions have inverses. An inverse function will allow a person to perform the opposite operation as the original function. The inverse function of addition is subtraction because it reverses what happened in the addition problem.

Operation:

4 + 2 = 6

Reverse:

6 - 2 = 4

The inverse of multiplication is division, the inverse of squared is the square root, and the inverse of the tangent function is the inverse tangent function (tan ^(-1)).

Inverse Tangent

The inverse tangent is the opposite of the tangent function. It is very useful when you know the sides of a right triangle but do not know the angle measure. The method for calculating the inverse tangent is as simple as using your scientific calculator.

The inverse tangent button is right above the tangent button, and you will most likely have to press the inverse key to get it, which makes it easier to remember.

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Examples

Now, let's go over some examples. Look at this image and see if you can find:

1.) What is the measure of angle A?

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Because you know the measure of the sides opposite and adjacent to the angle in question, we want to use the equation for tangent to solve for the angle measure.

tanΘ = opposite/adjacent

tanΘ = 13/9

tanΘ = 1.4444444

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