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If sin(x) = 1/√2, what is cos(x)?
If sin(x) = 1/√2, what is cos(x)?
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Practice Questions
1 question
Q1
If sin(x) = 1/√2, what is cos(x)?
1/√2
0
√2/2
1
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Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(x) = 1/√2, what is cos(x)?
Solution:
Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.
Steps: 8
Show Steps
Step 1: Start with the given equation: sin(x) = 1/√2.
Step 2: Recall the Pythagorean 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.
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