Question: If cos B = 1/2, what is the value of sin B?
Options:
√3/2
1/2
0
√2/2
Correct Answer: √3/2
Solution:
Using the identity sin^2 B + cos^2 B = 1, we have sin B = sqrt(1 - (1/2)^2) = sqrt(3/4) = √3/2.
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?
√3/2
1/2
0
√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.
Trigonometric Identities – Understanding and applying the Pythagorean identity sin² B + cos² B = 1 to find the sine of an angle when the cosine is known.
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