Exact trig values
Sine, cosine and tangent for the five angles that come out exactly — 0, 30, 45, 60 and 90 degrees — set beside the two triangles they fall out of, so a value you forget can be rebuilt rather than guessed.
Reference chart
Exact trig values
45° · 45° · 90°
30° · 60° · 90°
| θ | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 12 | √32 | √33 |
| 45° | √22 | √22 | 1 |
| 60° | √32 | 12 | √3 |
| 90° | 1 | 0 | — |
The two triangles ARE the table. Every exact value on it is one side of these triangles over another, so a value you forget can be rebuilt — never just guessed. tan 90° has no value: a vertical line has run out of “adjacent” to divide by.
What's on this chart
Most angles give ugly decimals, but five of them give clean, exact answers, and those five turn up constantly. This chart lists sine, cosine and tangent for 0, 30, 45, 60 and 90 degrees — but it does not stop at the list. It draws the 45-45-90 and 30-60-90 triangles beside the table, because every value in the table is just one side of those triangles divided by another. Memory fades; the triangles do not.
Why this chart helps
The two triangles are worth knowing on their own. The 45-45-90 has two equal legs of 1 and a hypotenuse of √2, so sine and cosine of 45 are both √2 over 2. The 30-60-90 has sides 1, √3 and 2, which is where every √3 in the table comes from — sin 60 and cos 30 are both √3 over 2, the long leg over the hypotenuse.
More printable charts
- Trig ratios (SOH CAH TOA)
Print Match the angle to two sides, then read off the ratio. - Unit circle
Print Find the angle, then read the point it lands on. - Radians and degrees
Print Find the degrees and read the radians beside them. - Law of sines and cosines
Print Pick the rule that fits the sides and angles known.