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If cos(x) = 1/2, what is the value of sin(x)?
If cos(x) = 1/2, what is the value of sin(x)?
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Practice Questions
1 question
Q1
If cos(x) = 1/2, what is the value of sin(x)?
√3/2
1/2
0
√2/2
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Using the identity sin^2(x) + cos^2(x) = 1, we have sin^2(x) = 1 - (1/2)^2 = 1 - 1/4 = 3/4. Therefore, sin(x) = √(3/4) = √3/2.
Questions & Step-by-step Solutions
1 item
Q
Q: If cos(x) = 1/2, what is the value of sin(x)?
Solution:
Using the identity sin^2(x) + cos^2(x) = 1, we have sin^2(x) = 1 - (1/2)^2 = 1 - 1/4 = 3/4. Therefore, sin(x) = √(3/4) = √3/2.
Steps: 10
Show Steps
Step 1: Start with the given information: cos(x) = 1/2.
Step 2: Use the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
Step 3: Substitute cos(x) into the identity: sin^2(x) + (1/2)^2 = 1.
Step 4: Calculate (1/2)^2: (1/2)^2 = 1/4.
Step 5: Rewrite the equation: sin^2(x) + 1/4 = 1.
Step 6: Subtract 1/4 from both sides: sin^2(x) = 1 - 1/4.
Step 7: Calculate 1 - 1/4: 1 - 1/4 = 3/4.
Step 8: Now we have sin^2(x) = 3/4.
Step 9: Take the square root of both sides: sin(x) = √(3/4).
Step 10: Simplify √(3/4): sin(x) = √3/2.
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