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If cos B = 1/2, what is the value of sin B?

Practice Questions

Q1
If cos B = 1/2, what is the value of sin B?
  1. √3/2
  2. 1/2
  3. 0
  4. √2/2

Questions & Step-by-Step Solutions

If cos B = 1/2, what is the value of sin B?
  • Step 1: Start with the given value, cos B = 1/2.
  • Step 2: Use the Pythagorean identity, which states that sin^2 B + cos^2 B = 1.
  • Step 3: Substitute the value of cos B into the identity: sin^2 B + (1/2)^2 = 1.
  • Step 4: Calculate (1/2)^2, which is 1/4.
  • Step 5: Now the equation looks like this: sin^2 B + 1/4 = 1.
  • Step 6: To isolate sin^2 B, subtract 1/4 from both sides: sin^2 B = 1 - 1/4.
  • Step 7: Calculate 1 - 1/4, which equals 3/4.
  • Step 8: Now we have sin^2 B = 3/4.
  • Step 9: To find sin B, take the square root of both sides: sin B = sqrt(3/4).
  • Step 10: Simplify sqrt(3/4) to get sin B = √3/2.
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