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What is the value of sin(tan^(-1)(1))?

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Question: What is the value of sin(tan^(-1)(1))?

Options:

  1. 1/√2
  2. 1/2
  3. 1
  4. √2/2

Correct Answer: √2/2

Solution: 

sin(tan^(-1)(1)) = √2/2

What is the value of sin(tan^(-1)(1))?

Practice Questions

Q1
What is the value of sin(tan^(-1)(1))?
  1. 1/√2
  2. 1/2
  3. 1
  4. √2/2

Questions & Step-by-Step Solutions

What is the value of sin(tan^(-1)(1))?
  • Step 1: Understand that tan^(-1)(1) means we are looking for an angle whose tangent is 1.
  • Step 2: Recall that the tangent of 45 degrees (or Ο€/4 radians) is 1.
  • Step 3: Therefore, tan^(-1)(1) = 45 degrees (or Ο€/4 radians).
  • Step 4: Now, we need to find the sine of 45 degrees (or Ο€/4 radians).
  • Step 5: The sine of 45 degrees is known to be √2/2.
  • Step 6: Thus, sin(tan^(-1)(1)) = sin(45 degrees) = √2/2.
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