Question: If x = sin^(-1)(1/3), then what is the value of cos(x)?
Options:
√(8)/3
√(2)/3
1/3
2/3
Correct Answer: √(8)/3
Solution:
Using the identity cos(x) = √(1 - sin^2(x)), we find cos(sin^(-1)(1/3)) = √(1 - (1/3)^2) = √(8)/3.
If x = sin^(-1)(1/3), then what is the value of cos(x)?
Practice Questions
Q1
If x = sin^(-1)(1/3), then what is the value of cos(x)?
√(8)/3
√(2)/3
1/3
2/3
Questions & Step-by-Step Solutions
If x = sin^(-1)(1/3), then what is the value of cos(x)?
Step 1: Understand that x = sin^(-1)(1/3) means that sin(x) = 1/3.
Step 2: Use the identity cos(x) = √(1 - sin^2(x)).
Step 3: Calculate sin^2(x). Since sin(x) = 1/3, we have sin^2(x) = (1/3)^2 = 1/9.
Step 4: Substitute sin^2(x) into the identity: cos(x) = √(1 - 1/9).
Step 5: Simplify the expression inside the square root: 1 - 1/9 = 9/9 - 1/9 = 8/9.
Step 6: Now, we have cos(x) = √(8/9).
Step 7: Simplify √(8/9) to √8 / √9 = √8 / 3.
Step 8: The final answer is cos(x) = √8 / 3.
Inverse Trigonometric Functions – Understanding how to use inverse trigonometric functions to find angles and their corresponding trigonometric values.
Pythagorean Identity – Applying the identity cos(x) = √(1 - sin^2(x)) to relate sine and cosine values.
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