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If x = sin^(-1)(3/5), what is the value of cos(x)?
If x = sin^(-1)(3/5), what is the value of cos(x)?
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Q1
If x = sin^(-1)(3/5), what is the value of cos(x)?
4/5
3/5
2/5
1/5
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Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.
Questions & Step-by-step Solutions
1 item
Q
Q: If x = sin^(-1)(3/5), what is the value of cos(x)?
Solution:
Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.
Steps: 7
Show Steps
Step 1: Understand that x = sin^(-1)(3/5) means that sin(x) = 3/5.
Step 2: Use the identity cos(x) = sqrt(1 - sin^2(x)).
Step 3: Calculate sin^2(x) which is (3/5)^2 = 9/25.
Step 4: Substitute sin^2(x) into the identity: cos(x) = sqrt(1 - 9/25).
Step 5: Simplify 1 - 9/25. Convert 1 to a fraction: 1 = 25/25, so 25/25 - 9/25 = 16/25.
Step 6: Now, cos(x) = sqrt(16/25).
Step 7: Calculate the square root: sqrt(16/25) = sqrt(16) / sqrt(25) = 4/5.
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