Trigonometry — SOH-CAH-TOA & Standard Values
The three ratios, the SOH-CAH-TOA memory trick, the standard-angle table, and the key identity.
By the PadhoDost Team · 📖 6 min read · Updated 4 August 2026
Part of Class 10 (CBSE) prep🧠 Three sides, three ratios
In a right triangle, name the sides relative to an angle θ: the side across from θ is 'Opposite', the one beside it is 'Adjacent', and the longest (the slope) is the 'Hypotenuse'. Trigonometry is just ratios of these three sides.
The memory trick: SOH-CAH-TOA
sin θ = O/H cos θ = A/H tan θ = O/A
Standard values (memorise these)
| θ | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | ∞ |
💡 Notice cos is just sin read backwards. Memorise the sin row and you get the cos row for free.
The identity you'll use everywhere
sin²θ + cos²θ = 1
⚡ Quick check
The value of tan 45° is:
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