Cosine Calculator — cos(x) in Degrees or Radians
cos(x)
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Angle in Degrees
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Angle in Radians
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Understanding the Cosine Function
The cosine function returns the ratio of the adjacent side to the hypotenuse in a right triangle. Like sine, it produces values between -1 and 1 with a period of 360 degrees. Cosine is an even function: cos(-x) = cos(x).
Key values: cos(0) = 1, cos(30) = sqrt(3)/2, cos(45) = sqrt(2)/2, cos(60) = 0.5, cos(90) = 0. The cosine function leads the sine function by 90 degrees: cos(x) = sin(90 - x).
Cosine is essential in physics, engineering, and computer graphics. It appears in the dot product formula, Fourier transforms, rotation matrices, and the law of cosines for solving triangles.
Frequently Asked Questions
What is cos(0)?
cos(0) = 1. This is the maximum value of the cosine function. At 0 degrees, the adjacent side equals the hypotenuse.
How are sine and cosine related?
Cosine is the complement of sine: cos(x) = sin(90-x). Also, sin^2(x) + cos^2(x) = 1 for all angles. They are phase-shifted versions of the same wave.
When is cosine negative?
Cosine is negative when the angle is between 90 and 270 degrees (second and third quadrants). This corresponds to positions on the left half of the unit circle.