Cosine Calculator
Calculate the cosine (cos) of an angle in different units.
Graph
Cosine Function
The cosine function is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Properties:
- Domain: All real numbers
- Range: [-1, 1]
- Period: 2π
- \(\cos(-\theta) = \cos(\theta)\) (Even function)
- \(\cos(\theta + 2\pi) = \cos(\theta)\)
Common Values:
- \(\cos(0) = 1\)
- \(\cos(\frac{\pi}{2}) = 0\)
- \(\cos(\pi) = -1\)
- \(\cos(\frac{3\pi}{2}) = 0\)
- \(\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}\)
- \(\cos(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}\)
- \(\cos(\frac{\pi}{3}) = \frac{1}{2}\)
Applications:
- Trigonometry
- Physics (wave motion, oscillations)
- Engineering (signal processing, AC circuits)
- Navigation and surveying
- Computer graphics and animation
- Sound and music theory
Geometric Interpretation:
- Ratio of adjacent side to hypotenuse in a right triangle
- x-coordinate of a point on the unit circle
- Even function (symmetric about y-axis)
- Periodic with period 2π
- Maximum value of 1 at θ = 0, 2π, 4π, ...
- Minimum value of -1 at θ = π, 3π, 5π, ...