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What is the value of cos(2x) if sin x = 1/2?
Practice Questions
Q1
What is the value of cos(2x) if sin x = 1/2?
1/2
0
1
√3/2
Questions & Step-by-Step Solutions
What is the value of cos(2x) if sin x = 1/2?
Steps
Concepts
Step 1: Identify the given value. We know that sin x = 1/2.
Step 2: Recall the double angle formula for cosine: cos(2x) = 1 - 2sin^2 x.
Step 3: Substitute the value of sin x into the formula. Since sin x = 1/2, we calculate sin^2 x: (1/2)^2 = 1/4.
Step 4: Now substitute sin^2 x back into the formula: cos(2x) = 1 - 2*(1/4).
Step 5: Calculate 2*(1/4) which equals 1/2.
Step 6: Now substitute this value back into the equation: cos(2x) = 1 - 1/2.
Step 7: Finally, calculate 1 - 1/2 to get cos(2x) = 1/2.
No concepts available.
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