Graph of y = cos(x)
Interactive graph of y = cos(x). Explore the cosine wave, its phase relationship to sine, and key properties with our free graphing calculator.
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Understanding the Function
The cosine function y = cos(x) is a periodic wave identical in shape to the sine function but shifted left by pi/2 radians. It starts at its maximum value of 1 when x = 0, then oscillates between -1 and 1 with a period of 2pi.
Cosine is an even function, meaning cos(-x) = cos(x), giving it mirror symmetry about the y-axis. Together with sine, it forms the foundation of trigonometry and is essential for describing circular motion, wave interference, and projections of rotating objects.
Key properties: amplitude of 1, period of 2pi, y-intercept at (0, 1), zeros at pi/2 + n*pi for every integer n. The derivative is -sin(x), and it satisfies the Pythagorean identity sin²(x) + cos²(x) = 1.