Introduction to Sine, Cosine, and Tangent (SOHCAHTOA)
Meet the three primary trigonometric ratios and learn the famous acronym used to remember them for a lifetime.
Trigonometry ratios describe the relationship between the angles and sides of a right triangle. The three main ratios are Sine, Cosine, and Tangent. Use the acronym SOH CAH TOA to remember them:
- SOH: \(\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}\)
- CAH: \(\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}\)
- TOA: \(\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\)
A triangle has sides 3, 4, and 5. Find the ratios for the angle \(\theta\) opposite the side of length 3.
- \(\sin(\theta) = \frac{3}{5} = 0.6\)
- \(\cos(\theta) = \frac{4}{5} = 0.8\)
- \(\tan(\theta) = \frac{3}{4} = 0.75\)
A ratio like \(\sin(\theta) = 0.5\) doesn't have units (like inches or cm). It simply means the opposite side is exactly half as long as the hypotenuse, no matter the size of the triangle.
If you know the angle of the sun and the length of a shadow, you can use the Tangent ratio (Opposite / Adjacent) to find the height of a building without ever climbing it!
Calculator Connection
The Trig Functions calculator gives you the decimal value for any angle, saving you from having to look them up in old-fashioned math tables.
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