Arctan 0

The value of arctan 0 is 0 degrees (or 0 radians). This is because tan 0° = 0 and tan 0^c (0 radians) = 0. Let us learn more about arctan 0 in different ways.

The value of arctan 0 is 0. Since the other name of arctan is "tan inverse", we can say that tan inverse 0 is 0. Since 0 degrees is same as 0 radians:

• arctan 0 in degrees is 0°.
• arctan 0 in radians is 0^c.

i.e., arctan 0 = tan inverse 0 = 0° (or) 0^c. Let us see how to find this in different ways.

We study about the unit circle in trigonometry. Every point on the unit circle corresponds to some angle (θ) and its coordinates would be (cos θ, sin θ). i.e., its x-coordinate represents the cosine of the angle θ and its y-coordinate represents the sine of the angle θ. Let us just take a look at the unit circle.

Let us assume that arctan 0 = x ... (1)

Then by the definition of arctan, tan x = 0. Using the formula of tan, (sin x)/(cos x) = 0. 0 can be written as 0/1. So we have to see for what value of x, we get (sin x) / (cos x) = 0/1. i.e., we should check the unit circle for what value of x, we get

• sin x = 0 and
• cos x = 1

These both are happening in the unit circle only when x = 0° (or) 0^c. Substituting this in (1), we get arctan 0 = 0° (or) 0^c.

Let us take a look at the trigonometric table of values.

From the definition of inverse function, if f^-1(x) = y then f(y) = x. i.e., To find tan inverse 0, we have to see the tan of what angle is equal to 0. In the above table we can see that:

• tan 0° = 0
• tan 180° = 0
• tan 360° = 0 and so on

So we is arctan x (or) tan inverse of x = 0°, 180°, 360°, ... ? No, because the range of arctan x is (-90°, 90°). But the angles 180°, 360°, ... do not fall in this range. Only the angle 0° falls in the range of tan inverse x. Hence,

tan inverse 0 = 0°

Since 0° is same as 0 radians, we have tan inverse x = 0^c.

Therefore, tan inverse 0 = 0° (OR) 0^c.

Important Notes on Arctan 0:

• arc tan 0 = 0
• This can also be written as tan inverse 0 = 0 (or) tan^-1 = 0.

☛ Related Topics:

• Arctan 0 Calculator
• Inverse Tangent Calculator

What is the Value of Arctan 0?

The value of arctan 0 is 0 degrees. Since 0 degrees is same as 0 radians, we can say arctan 0 = 0 radians as well. Thus, arctan 0 = 0 degrees (or) 0 radians.

Is Arctan 0 0 or Pi?

Of course, we know that tan 0 = 0 and tan π = 0 as well. But while finding arctan 0, we say that its value is 0 (but not π) because the range of arctan x is (-π/2, π/2) and hence the value of arc tan 0 should fall in this range.

How to Find Arc Tan 0 Using Unit Circle With Tangent?

To see what is the unit circle with a tangent, click here. From this, tan 0 = 0 (where the 0 next to tan can be in radians or degrees). Thus, arctan 0 = 0 radians or 0 degrees.

What is Tan Inverse in Terms of Pi?

We know that tan^-1 0 = 0 degrees. To convert degrees into radians, we multiply the angle by π/180. So tan^-10 = 0 × π/180 radians = 0 radians. So the question must be asking what is the value of tan^-10 in radians and the answer is 0.

Why is Arctan 0 Not Pi?

Arc tan 0 = 0 but not pi. Though both values of tan 0 and tan π are equal to 0, we say that arctan 0 = 0. This is because the range of the inverse tan function is (-π/2, π/2).

What is Arctan 0 in Degrees?

We know that sin 0° = 0 and cos 0° = 0. Also, we know that tan 0° = (sin 0°) / (cos 0°) = 0/0 = 0. Thus, tan 0° = 0. Then by the definition of inverse function, arctan 0 = 0°.