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Evaluate the expression sin^(-1)(1) + cos^(-1)(0).

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Question: Evaluate the expression sin^(-1)(1) + cos^(-1)(0).

Options:

  1. π/2
  2. π
  3. 0
  4. 1

Correct Answer: π/2

Solution: 

sin^(-1)(1) = π/2 and cos^(-1)(0) = π/2. Therefore, π/2 + π/2 = π.

Evaluate the expression sin^(-1)(1) + cos^(-1)(0).

Practice Questions

Q1
Evaluate the expression sin^(-1)(1) + cos^(-1)(0).
  1. π/2
  2. π
  3. 0
  4. 1

Questions & Step-by-Step Solutions

Evaluate the expression sin^(-1)(1) + cos^(-1)(0).
  • Step 1: Understand the notation sin^(-1)(1) and cos^(-1)(0). This means we are looking for the angles whose sine is 1 and whose cosine is 0.
  • Step 2: Find sin^(-1)(1). The sine of π/2 (90 degrees) is 1. So, sin^(-1)(1) = π/2.
  • Step 3: Find cos^(-1)(0). The cosine of π/2 (90 degrees) is 0. So, cos^(-1)(0) = π/2.
  • Step 4: Add the results from Step 2 and Step 3. We have π/2 + π/2.
  • Step 5: Simplify π/2 + π/2. This equals π.
  • Inverse Trigonometric Functions – Understanding the values of sin^(-1)(x) and cos^(-1)(x) for specific inputs.
  • Addition of Angles – Adding the results of inverse trigonometric functions to find a final value.
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