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If sin(x) = 1/√2, what is the value of cos(x)?
Practice Questions
Q1
If sin(x) = 1/√2, what is the value of cos(x)?
1/√2
0
√2/2
1
Questions & Step-by-Step Solutions
If sin(x) = 1/√2, what is the value of cos(x)?
Correct Answer: 1/√2
Steps
Concepts
Step 1: Start with the given equation: sin(x) = 1/√2.
Step 2: Use the identity sin^2(x) + cos^2(x) = 1.
Step 3: Calculate sin^2(x): (1/√2)^2 = 1/2.
Step 4: Substitute sin^2(x) into the identity: 1/2 + cos^2(x) = 1.
Step 5: Rearrange the equation to find cos^2(x): cos^2(x) = 1 - 1/2.
Step 6: Simplify the right side: cos^2(x) = 1/2.
Step 7: Take the square root of both sides to find cos(x): cos(x) = ±√(1/2).
Step 8: Simplify √(1/2) to get cos(x) = ±1/√2.
No concepts available.
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