Question: If cos B = 0.6, what is the value of sin B?
Options:
0.8
0.6
0.4
0.2
Correct Answer: 0.8
Solution:
Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.
If cos B = 0.6, what is the value of sin B?
Practice Questions
Q1
If cos B = 0.6, what is the value of sin B?
0.8
0.6
0.4
0.2
Questions & Step-by-Step Solutions
If cos B = 0.6, what is the value of sin B?
Step 1: Start with the given value of cos B, which is 0.6.
Step 2: Use the Pythagorean identity, which states that sin²B + cos²B = 1.
Step 3: Rearrange the identity to find sin²B: sin²B = 1 - cos²B.
Step 4: Calculate cos²B: cos²B = (0.6)² = 0.36.
Step 5: Substitute the value of cos²B into the equation: sin²B = 1 - 0.36.
Step 6: Calculate 1 - 0.36, which equals 0.64.
Step 7: Now, take the square root of 0.64 to find sin B: sin B = √(0.64).
Step 8: Calculate the square root of 0.64, which is 0.8.
Pythagorean Identity – The relationship between sine and cosine, specifically sin²B + cos²B = 1, which allows for the calculation of one function if the other is known.
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