The topic I want to deal with is about trigonometry and more specifically **How to obtain the Tangent inverse of a value on a calculator?**

## What is Tangent Inverse?

The tangent inverse or ArcTan is the inverse function of the tangent of an angle.

To find the arc tangent of a number, there are several ways, and we will always need any scientific calculator.

Suppose we need to find the inverse tangent of the following number: **0.707106**

Then, using the calculator, we must keep in mind that option **“D”** must be enabled at the top of the screen, which means that the angle mode of the calculator is in degrees minutes and seconds.

Now we must type the shift key , at the top left of the screen the letter **“S”** is shown.

This option activates the change function of each calculator key. Usually, the second function of each calculator key is displayed in an opaque color next to the main key.

For the example, you must activate the second function of the calculator tangent key **“tan”** which is **“tan⁻¹**” which is the inverse tangent function. The label **“tan⁻¹**” will appear on the calculator display.

Now type in the value: **0.707106** and press the equal key, which corresponds to a value of **35.26435984** on the calculator screen.

The previous number is an angle but it is in a decimal representation, so to know its value in degrees minutes and seconds, it is necessary to press again the **“shift”** key, and the key of degrees minutes and seconds. The calculator then shows the value **35°15’51.7″** on the screen, that is, the complete angle with its degrees, minutes and seconds.

To know the inverse sine or the inverse cosine of any number, the procedure is the same as above, except that if it is a inverse sine, we use the sin key and its inverse, and likewise, if it is a inverse cosine, we use the cos key and its inverse.

## What to do if the calculator does not have the degrees, minutes and seconds key?

As is the case with some cell phones or the Windows calculator?

Then as a first step we calculate the inverse tangent of the number and proceed like this:

**ArcTan = 35.26435984**

Take the decimal part of the previous value **(35.26435984)** = **0.26435984 **and multiply it by **60** which is equal to **15.8615904** which means that the whole part of this number, or **15**, is the minutes of the angle. Up to there we would have: **35°15′**.

From the previous number **(15.8615904)**, we take again the decimal part **0.8615904** and again it is multiplied by **60** which is equal to **51.695424** which are the seconds of the angle and can be approximated to **51.7**

Finally, the angle converted to degrees, minutes and seconds is: **35°15’51.7″**

So: ArcTan **0.707106** is **35.26435984** and is equal to **35°15’51,7″**.

This is all, really it is a simple and easy to understand item. You might also be interested: **Conversion Between Millimeters and Inches**

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