Sine value (sin θ)
± 0.8660
This calculator finds the value of the sine of an angle (sin θ) when you know its cosine (cos θ). The calculation is based on the Pythagorean identity, a fundamental rule in trigonometry.
Formula Used
The Pythagorean identity is sin²θ + cos²θ = 1. To find the sine, we rearrange this formula:
sin θ = ±√(1 - cos²θ)
The plus-minus sign (±) indicates that for a given cosine value, there are two possible results for the sine (one positive and one negative), corresponding to angles in different quadrants of the unit circle.
Example
Let's calculate the sine when the cosine is 0.5.
- Given Cosine: cos θ = 0.5
- Step 1: Square the cosine value: 0.5² = 0.25
- Step 2: Subtract the result from 1: 1 - 0.25 = 0.75
- Step 3: Find the square root of the result: √0.75 ≈ 0.8660
- Result: sin θ = ±0.8660