Calculate the sine 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 sine is a fundamental trigonometric function. In a right-angled triangle, the sine of an acute angle is the ratio of the length of the side opposite the angle to the hypotenuse: sin(θ) = Opposite / Hypotenuse.
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = y_{\text{unit circle}}On the unit circle (radius 1), sine corresponds directly to the vertical y-coordinate of the terminal angle point.
Scenario: Calculate sin(30°)
Given: θ = 30° = π / 6 radians
In a 30°-60°-90° triangle, the side opposite 30° is half the hypotenuse.
sin(30°) = 1 / 2 = 0.5
sin(0°) = 0, sin(30°) = 1/2, sin(45°) = √2/2, sin(60°) = √3/2, sin(90°) = 1.
The sine wave repeats its cycle every 360° or 2π radians: sin(θ + 2π) = sin(θ).
Multiply degrees by π / 180: radians = degrees × (π / 180).
The reciprocal of sine is cosecant: csc(θ) = 1 / sin(θ).
Calculate the cosine 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.