Trigonometry⏱ 6 min read

Sine, Cosine & Tangent

SOH · CAH · TOA

📖 What are Sin, Cos, and Tan?

These are the three fundamental trigonometric ratios. For a right triangle with angle θ, they describe the relationship between the angle and the ratios of the triangle's sides:

sin θ
SOH
= Opposite / Hypotenuse
cos θ
CAH
= Adjacent / Hypotenuse
tan θ
TOA
= Opposite / Adjacent

🔤 The Sides of a Right Triangle

Hyp
HypotenuseThe longest side — always opposite the right angle
Opp
OppositeThe side directly across from the angle θ
Adj
AdjacentThe side next to the angle θ (not the hypotenuse)

📝 Step-by-Step Example

A right triangle has a hypotenuse of 10 and opposite side of 6. Find the angle θ.

1
We know Opposite and Hypotenuse → use sinsin θ = O / H = 6 / 10 = 0.6
2
Use inverse sin (sin⁻¹) to find the angleθ = sin⁻¹(0.6)
Answer: θ ≈ 36.87°

📊 Common Angle Values

Angle sin cos tan
010
30°½√3/21/√3
45°√2/2√2/21
60°√3/2½√3
90°10undefined
Advertisement

🎯 Quick Fact

The word "sine" comes from the Latin "sinus", meaning "bay" or "fold" — early mathematicians used a folded piece of paper to measure it!