How to solve
Because a unit-circle point (cos θ, sin θ) lies on x² + y² = 1, the squares of sine and cosine always add to 1. Given one, you recover the other (up to sign) by rearranging and taking a square root.
Steps
- Isolate the unknown square: e.g. cos²θ = 1 − sin²θ.
- Take the square root to recover the absolute value.
- Apply the given quadrant or sign information when provided.
Example
If sin θ = 3/5 and θ is in quadrant I, find cos θ.
- cos²θ = 1 − (3/5)² = 1 − 9/25 = 16/25.
- cos θ = ±4/5; quadrant I forces the positive value.
- cos θ = 4/5.
Answer: 4/5
How to type answers
- Enter a simplified fraction or sqrt form like sqrt(3)/2
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