Sine Calculator
Calculate the sine of an angle and visualize the function.
Function Plot
Sine Function
The sine function is defined as:
\[ \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Properties:
- Domain: All real numbers
- Range: [-1, 1]
- Period: 2π (360°)
- Odd function: sin(-x) = -sin(x)
- Amplitude: 1
Common Values:
- \[ \sin(0°) = 0 \]
- \[ \sin(30°) = \frac{1}{2} \]
- \[ \sin(45°) = \frac{1}{\sqrt{2}} \approx 0.7071 \]
- \[ \sin(60°) = \frac{\sqrt{3}}{2} \approx 0.8660 \]
- \[ \sin(90°) = 1 \]
Applications:
- Trigonometry
- Calculus
- Physics (wave motion)
- Engineering (signal processing)
- Music and sound analysis
Related Functions:
- \[ \sin(x) = \cos(90° - x) \]
- \[ \sin(x) = \frac{1}{\csc(x)} \]
- \[ \sin(x) = \frac{\tan(x)}{\sqrt{1 + \tan^2(x)}} \]
Special Angles:
- \[ \sin(0°) = 0 \]
- \[ \sin(90°) = 1 \]
- \[ \sin(180°) = 0 \]
- \[ \sin(270°) = -1 \]
- \[ \sin(360°) = 0 \]