sin θ = ±√(1 - cos² θ)
Sine is calculated using the fundamental trigonometric identity
Enter a decimal number (-1 ≤ cos θ ≤ 1), fraction (1/2), or expression with square root (√2/2)
Choose quadrant or show all solutions:
Calculate sine values from cosine inputs using the fundamental trigonometric identity. This calculator determines both possible sine values for any given cosine, as every cosine value corresponds to two angles in the unit circle.
sin θ = ±√(1 - cos² θ)
Key Features: Input cosine values as decimals, fractions (1/2), or expressions with square roots (√2/2). Select specific quadrants for targeted results or view all possible solutions simultaneously.
The calculator accepts cosine values between -1 and 1, supporting various input formats including exact values like √3/2 for precise trigonometric calculations. Results include corresponding angles in both degrees and radians, plus additional trigonometric values.
Example Calculation:
Input: cos θ = 0.5
Result: sin θ = ±0.8660 (which equals ±√3/2)
This corresponds to angles 60° and 120° (positive sine) or 240° and 300° (negative sine) in the standard position.
The integrated unit circle visualization shows the geometric relationship between cosine and sine values, helping understand quadrant-based sign variations and angle relationships in trigonometric functions.