Exact Trigonometric Values

Exact trigonometric values

The values of sine, cosine, and tangent for the angles $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $90^\circ$.

Learn these – standard triangles – and extend them to other ranges [note: tan 90 is not defined].

You should make sure you know the values listed, or that you can work them out quickly by drawing appropriate triangles. You should make sure you can identify them on a sketch of sin, cos or tan.

For 45 you can use the isosceles right-angled triangle:

And for the 30 and 60 ones, you can use half of an equilateral triangle with sides of length 2: