Sine, cosine and tangent
Three ratios linking an angle in a right-angled triangle to its sides: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.
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Analogy
SOH CAH TOA is a chant that reminds you which sides go with which ratio.
Example
Hypotenuse: opposite the right angleOpposite: facing your angleAdjacent: next to your angleUse SOH CAH TOA to pick the ratio
In practice
Surveyors use them to find heights and distances they cannot measure directly.
Practice
Flashcards
- What does SOH stand for?Sine = Opposite / Hypotenuse.
Questions people ask
How do you choose between sin, cos and tan?
Label the sides: hypotenuse, opposite and adjacent. Then see which two sides you have or need. If they are opposite and hypotenuse, use sin. If adjacent and hypotenuse, use cos. If opposite and adjacent, use tan. Writing SOH CAH TOA at the top of your working is a good habit under exam pressure.
Does trigonometry only work for right-angled triangles?
The basic SOH CAH TOA ratios only work in right-angled triangles. For other triangles you can use the sine rule and cosine rule, which are covered later, or split the triangle into two right-angled ones. Many real problems become right-angled once you draw a helpful vertical line.