Tangent Calculator
Calculate the tangent of an angle and visualize the function.
Function Plot
Tangent Function
The tangent function is defined as:
\[ \tan(x) = \frac{\sin(x)}{\cos(x)} = \frac{\text{opposite}}{\text{adjacent}} \]
Properties:
- Domain: All real numbers except \(x = \frac{\pi}{2} + n\pi\) (where n is an integer)
- Range: All real numbers
- Period: π (180°)
- Odd function: tan(-x) = -tan(x)
- Vertical asymptotes at \(x = \frac{\pi}{2} + n\pi\)
Common Values:
- \[ \tan(0°) = 0 \]
- \[ \tan(30°) = \frac{1}{\sqrt{3}} \approx 0.5774 \]
- \[ \tan(45°) = 1 \]
- \[ \tan(60°) = \sqrt{3} \approx 1.7321 \]
- \[ \tan(90°) = \text{undefined} \]
Applications:
- Trigonometry
- Calculus
- Physics (wave motion)
- Engineering (signal processing)
- Navigation and surveying
Related Functions:
- \[ \tan(x) = \frac{\sin(x)}{\cos(x)} \]
- \[ \tan(x) = \frac{1}{\cot(x)} \]
- \[ \tan(x) = \frac{\sec(x)}{\csc(x)} \]
Special Angles:
- \[ \tan(0°) = 0 \]
- \[ \tan(45°) = 1 \]
- \[ \tan(90°) = \text{undefined} \]
- \[ \tan(180°) = 0 \]
- \[ \tan(270°) = \text{undefined} \]