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Trigonometry

Trigonometric Ratios (sin, cos, tan)

Formula
sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent

What is Trigonometric Ratios (sin, cos, tan)?

In a right-angled triangle, the three basic trigonometric ratios relate the angles to the sides. Sin is opposite over hypotenuse, cos is adjacent over hypotenuse, and tan is opposite over adjacent.

Variables

  • θ
    θ — Angle in the right triangle
  • O
    Opposite — Side opposite to the angle
  • A
    Adjacent — Side adjacent to the angle
  • H
    Hypotenuse — Longest side (opposite the right angle)

Worked Examples

Example 1

In a right triangle, the opposite side is 3 and the hypotenuse is 5. Find sin θ.

Solution:

sin θ = 3/5 = 0.6

Frequently Asked Questions

Related Formulas

Law of Cosines

c² = a² + b² − 2ab × cos(C)

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)

Pythagorean Trigonometric Identities

sin²θ + cos²θ = 1

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