Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(x) = 3/5, what is cos(x)?
Solution: Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.
Steps: 11
Step 1: Start with the given information: sin(x) = 3/5.
Step 2: Use the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
Step 3: Calculate sin^2(x): (3/5)^2 = 9/25.
Step 4: Substitute sin^2(x) into the identity: 9/25 + cos^2(x) = 1.
Step 5: Rearrange the equation to find cos^2(x): cos^2(x) = 1 - 9/25.
Step 6: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
