If x = sin^(-1)(3/5), what is cos(x)?

If x = sin^(-1)(3/5), what is cos(x)?

Correct Answer: 4/5

Step 1: Understand that x = sin^(-1)(3/5) means that sin(x) = 3/5.
Step 2: Use the Pythagorean identity which states that cos^2(x) + sin^2(x) = 1.
Step 3: Substitute sin(x) into the identity: cos^2(x) + (3/5)^2 = 1.
Step 4: Calculate (3/5)^2, which is 9/25.
Step 5: Rewrite the equation: cos^2(x) + 9/25 = 1.
Step 6: To isolate cos^2(x), subtract 9/25 from both sides: cos^2(x) = 1 - 9/25.
Step 7: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
Step 8: Now, subtract: cos^2(x) = 25/25 - 9/25 = 16/25.
Step 9: Take the square root of both sides to find cos(x): cos(x) = √(16/25).
Step 10: Simplify the square root: cos(x) = 4/5.

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