The √ trick: Write √0/2, √1/2, √2/2, √3/2, √4/2 — that's sin 0°, 30°, 45°, 60°, 90°. For cos, read the same sequence BACKWARDS. For tan, divide sin by cos at each angle.
Trigonometry Table — Values of sin, cos, tan
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Items to Memorize
- sin 0° = 0
- sin 30° = 1/2
- sin 45° = √2/2
- sin 60° = √3/2
- sin 90° = 1
- cos 0° = 1
- cos 30° = √3/2
- cos 45° = √2/2
- cos 60° = 1/2
- cos 90° = 0
- tan 0° = 0
- tan 30° = 1/√3
- tan 45° = 1
- tan 60° = √3
- tan 90° = undefined
Mnemonic Tricks
How It Maps
| Cue | Maps To |
|---|---|
| √0/2 = 0 | sin 0° |
| √1/2 = 1/2 | sin 30° |
| √2/2 | sin 45° |
| √3/2 | sin 60° |
| √4/2 = 1 | sin 90° |
Why It Sticks
Instead of memorizing 15 values, you only remember one pattern: √(0,1,2,3,4)/2 for sin, then reverse for cos. Tan = sin/cos. Three rules replace an entire table.
Zero, half, root-two-by-two, root-three-by-two, then one — sin is done! Flip it back for cosine's run, divide for tan — now you've won!
Why It Sticks
A rhythm that walks through the sin values left-to-right, then tells you the two operations (reverse, divide) that generate the rest of the table. Three lines = complete table.
Frequently Asked Questions
What is the easiest trick to learn the trigonometry table?
The √ pattern: sin values for 0°,30°,45°,60°,90° = √0/2, √1/2, √2/2, √3/2, √4/2. Cos is the same sequence in reverse. Tan = sin÷cos. One pattern generates the entire table.
How to remember sin 30, sin 45, sin 60?
sin 30° = √1/2 = 1/2. sin 45° = √2/2 ≈ 0.707. sin 60° = √3/2 ≈ 0.866. The numerators go √1, √2, √3 — just count up under the root sign!
Why is cos the reverse of sin?
Because cos θ = sin(90° - θ). So cos 0° = sin 90° = 1, cos 30° = sin 60° = √3/2, etc. This complementary relationship means you only need to memorize one row.
What is tan 45°?
tan 45° = sin 45° / cos 45° = (√2/2) / (√2/2) = 1. This is why a 45° line has slope = 1. Geometrically, it's the angle where opposite and adjacent sides are equal.
Is the trigonometry table important for JEE and SSC?
Essential. JEE uses these values in calculus, coordinate geometry, and physics. SSC/Banking uses them in height-and-distance problems. Quick recall saves 30+ seconds per question.