If sin(θ) = 3/5, what is cos(θ)?

If sin(θ) = 3/5, what is cos(θ)?

Correct Answer: 4/5

Step 1: Start with the given information: sin(θ) = 3/5.
Step 2: Recall the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
Step 3: Substitute sin(θ) into the identity: (3/5)² + cos²(θ) = 1.
Step 4: Calculate (3/5)²: (3/5)² = 9/25.
Step 5: Replace sin²(θ) in the equation: 9/25 + cos²(θ) = 1.
Step 6: To isolate cos²(θ), subtract 9/25 from both sides: cos²(θ) = 1 - 9/25.
Step 7: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
Step 8: Now, subtract: cos²(θ) = 25/25 - 9/25 = 16/25.
Step 9: Take the square root of both sides to find cos(θ): cos(θ) = √(16/25).
Step 10: Simplify the square root: cos(θ) = 4/5.

Pythagorean Identity – The relationship between sine and cosine, specifically that sin²(θ) + cos²(θ) = 1.
Trigonometric Functions – Understanding the values of sine and cosine for angles in a right triangle.