sin Sin Cos Tan Calculator

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Understanding Sin, Cos, and Tan

Sine, cosine, and tangent are the three primary trigonometric ratios. They relate the angles of a right triangle to the ratios of its sides.

sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)

The Unit Circle

On the unit circle (radius = 1), for any angle θ: the x-coordinate = cos(θ) and the y-coordinate = sin(θ). This extends trig functions to all angles beyond 0°–90°.

Frequently Asked Questions

What is sin(30°)? ▼
sin(30°) = 0.5. This is one of the most commonly used trig values. sin(30°) = 1/2 exactly.
What is tan(45°)? ▼
tan(45°) = 1. At 45°, sin and cos are equal (both = √2/2), so their ratio equals 1.
Why is tan(90°) undefined? ▼
tan(90°) = sin(90°)/cos(90°) = 1/0, which is undefined. Division by zero is not defined in mathematics.