Calculate the cosine of any angle in degrees or radians. Shows unit circle coordinates, exact values for special angles, and step-by-step steps.
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In mathematics, the cosine is a fundamental trigonometric function. In a right triangle, the cosine of an acute angle is the ratio of the length of the adjacent leg to the hypotenuse: cos(θ) = Adjacent / Hypotenuse.
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = x_{\text{unit circle}}On the Cartesian unit circle of radius 1, cosine corresponds directly to the horizontal x-coordinate of the terminal point.
Scenario: Calculate cos(60°)
Given: θ = 60° = π / 3 radians
In a 30°-60°-90° triangle, the adjacent leg to 60° is half the hypotenuse.
cos(60°) = 1 / 2 = 0.5
cos(0°) = 1, cos(30°) = √3/2, cos(45°) = √2/2, cos(60°) = 1/2, cos(90°) = 0.
Sine and cosine are cofunctions: cos(θ) = sin(90° - θ). A cosine wave is a sine wave shifted 90° to the left.
The reciprocal of cosine is secant: sec(θ) = 1 / cos(θ).
At 90°, the terminal ray points vertically straight up along the y-axis, where the horizontal x-coordinate is 0.
Calculate the sine of any angle in degrees or radians. Shows unit circle coordinates, exact values for special angles, and step-by-step steps.
Calculate the tangent of any angle in degrees or radians. Identifies vertical asymptotes, exact values for special angles, and ratios.
Calculate the cotangent of any angle in degrees or radians. Identifies undefined points, exact values for special angles, and reciprocal trig.