If x = sin^(-1)(1/√2), then what is the value of cos(x)?

1 question

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Q: If x = sin^(-1)(1/√2), then what is the value of cos(x)?

Solution: If x = sin^(-1)(1/√2), then sin(x) = 1/√2. Therefore, cos(x) = √(1 - sin^2(x)) = √(1 - (1/√2)^2) = √(1/2) = √2/2.

Steps: 9

Step 1: Understand that x = sin^(-1)(1/√2) means that sin(x) = 1/√2.
Step 2: Recall the Pythagorean identity which states that sin^2(x) + cos^2(x) = 1.
Step 3: Substitute sin(x) into the identity: sin^2(x) = (1/√2)^2.
Step 4: Calculate (1/√2)^2, which equals 1/2.
Step 5: Now, use the identity: 1/2 + cos^2(x) = 1.
Step 6: Rearrange the equation to find cos^2(x): cos^2(x) = 1 - 1/2.
Step 7: Calculate 1 - 1/2, which equals 1/2.
Step 8: Now, take the square root to find cos(x): cos(x) = √(1/2).
Step 9: Simplify √(1/2) to get √2/2.