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If x = tan^(-1)(1), what is the value of x?

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Question: If x = tan^(-1)(1), what is the value of x?

Options:

  1. π/4
  2. π/3
  3. π/6
  4. 0

Correct Answer: π/4

Solution: 

tan^(-1)(1) = π/4, since tan(π/4) = 1.

If x = tan^(-1)(1), what is the value of x?

Practice Questions

Q1
If x = tan^(-1)(1), what is the value of x?
  1. π/4
  2. π/3
  3. π/6
  4. 0

Questions & Step-by-Step Solutions

If x = tan^(-1)(1), what is the value of x?
Correct Answer: π/4
  • Step 1: Understand that tan^(-1)(1) means we are looking for an angle whose tangent is 1.
  • Step 2: Recall that the tangent function (tan) gives the ratio of the opposite side to the adjacent side in a right triangle.
  • Step 3: Remember that tan(Ï€/4) equals 1. This means that at an angle of Ï€/4 radians (or 45 degrees), the tangent value is 1.
  • Step 4: Therefore, since tan^(-1)(1) asks for the angle whose tangent is 1, we conclude that x = Ï€/4.
  • Inverse Trigonometric Functions – Understanding how to evaluate inverse trigonometric functions, specifically the arctangent function.
  • Trigonometric Values – Knowledge of standard angles and their corresponding trigonometric values, particularly that tan(Ï€/4) = 1.
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