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Arctan 2

The value of arctan 2 in degrees is 63.435° and in radians is 1.107 (both values are rounded to 3 decimals). Let us see how to find the value of arctan 2 and also let us solve a few examples using this value.

1.	What is Arctan 2?
2.	How to Find the Value of Tan^-1 2?
3.	FAQs on Arctan 2

What is Arctan 2?

The value of arctan 2 is 63.435 degrees (or) 1.107 radians. We know that the angle in degrees can be converted into radians by multiplying it by π/180 and the angle in radians can be converted into degrees by multiplying it by 180/π. Thus,

Let us convert degrees into radians. arctan 2 ≈ 63.435° = 63.435 × π/180 ≈ 1.107 radians
Let us convert radians into degrees. arctan 2 ≈ 1.107 = 1.107 × 180/π ≈ 63.435 degrees

arctan 2 (or) inverse tan 2 (or) tan^-1 2

There might be slight variations in the above calculations as the above two values are the values of arctan 2 rounded to 3 decimals. But in fact, arctan 2 is an irrational number and its value is non-terminating (and also, it has a non-repeating pattern of decimals). i.e.,

arctan 2 ≈ 63.434964992129578476426200304282...
arctan 2 ≈ 1.1071487177940905030170654601785...

How to Find the Value of Tan^-1 2?

We usually find the values of arctan using the unit circle or trigonometric table. But 2 is not present in both. Thus, we need to use the "arctan" (or) tan^-1button on the calculator to find arctan 2. Follow the steps below to find the value of arctan 2.

Finding Arctan 2 in Degrees

Set the calculator in degrees mode.
Press the "arctan" button (or) "tan^-1" button (or) a combination of "inv" and "tan" buttons (whatever is available on your calculator).
Type the number "2".
Then it will show the value of arctan 2 in degrees to be 63.434964992129578476426200304282...

Finding Arctan 2 in Radians

Just set the calculator in radians mode and use the same process as above. Then we will get the value of arctan 2 in radians to be 1.1071487177940905030170654601785...

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Arctan 2 Examples

Example 1: Prove that arctan 0 + arctan 2 = arctan 2.

Solution:

We know that arctan 0 = 0 and adding 0 to any number results in the number itself. Thus,

arctan 0 + arctan 2 = arctan 2

Answer: The given equation is proved.
Example 2: Find the angle (in radians) in the first quadrant that satisfies the equation tan x = 2.

Solution:

The given trigonometric equation is tan x = 2.

From this, x = arctan 2.

Using the calculator, x ≈ 1.107 radians and this lies in the first quadrant (As it lies between 0 and π/2).

Answer: 1.107 radians.
Example 3: What is the general solution of the equation given in Example 2?

Solution:

The given equation is tan x = 2 and we found that arctan 2 = 1.107 radians.

We know that the general solution of a trigonometric equation of tan is of the form nπ + x.

Hence, the general solution is nπ + 1.107.

Answer: nπ + 1.107

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Practice Questions on Arctan 2

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FAQs on Arctan 2

What is the Value of Arctan 2 in Degrees?

The value of arctan 2 in degrees is approximately equal to 63.435 when rounded to 3 decimals. To find this, set the calculator in degrees mode first.

What is Inverse Tan 2 in Radians?

The value of arctan 2 in radians is approximately equal to 1.107 when rounded to 3 decimals. To find this, keep the calculator in radians mode first.

Is Tan^-1 2 Rational and Irrational?

If we calculate tan^-12 in degrees mode, we get 63.434948822922010648427806279547... The pattern is non-repeating and non-terminating. So tan^-12 is irrational.

Tan Arctan 2 Equal to Cot 2?

No, because arctan 2 = 1.107 radians and cot 2 = -0.457 (when 2 is in radians). Note that arctan is not the same as cot.

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