What is the value of arctan 0 in degrees?
Understand the Problem
The question is asking for the value of the arctangent of 0 expressed in degrees. The arctangent function returns the angle whose tangent is the given number, and in this case, we need to find the angle corresponding to the tangent value of 0.
Answer
$0^\circ$
Answer for screen readers
The value of the arctangent of 0 expressed in degrees is $0^\circ$.
Steps to Solve
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Identify the tangent function To solve for the angle whose tangent is 0, we need to recall that tangent is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
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Determine the angle with tangent equal to 0 The value of tangent is 0 when the opposite side is 0, which occurs at an angle of 0 degrees. Thus, we can establish the equation: $$ \tan(\theta) = 0 $$
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Apply the arctangent function Using the arctangent function, we find: $$ \theta = \arctan(0) $$ By the definition of the arctangent, this gives us the angle.
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Convert the angle to degrees The result from the arctangent can be directly expressed in degrees, and we find: $$ \theta = 0^\circ $$
The value of the arctangent of 0 expressed in degrees is $0^\circ$.
More Information
The arctangent function, also known as $\tan^{-1}$, is used to determine the angle when the value of the tangent is known. In this case, arctangent of 0 directly corresponds to an angle of 0 degrees.
Tips
- Assuming the arctangent of 0 corresponds to angles other than 0 degrees. Remember, the tangent function only equals 0 at angles like 0 degrees, which is the principal value for arctangent.
