Why sin(30˚) equals 1/2

Using some simple geometry, Pythagoras' Theorem and laws of trigonometry, we can easily derive the exact values for sine, cosine and tangent of the angles of 30˚, 45˚ and 60˚.

You may have been expected to remember values such as sin(30˚) = 1/2, sin(45˚) = √2/2, sin(60˚) = √3/2. Unfortunately, this is pretty boring stuff to try and remember.

What's far more interesting however, is where these values come from. In deriving the results, you will also gain a better understanding of how trigonometry works.

For the angle of 45˚, we use a 45˚-45˚-90˚ triangle to derive the results.

For the angles of 30˚ and 60˚, we use a 30˚-60˚-90˚ triangle to derive the results.