This subsection is not completed yet, but in the meantime here are some practice questions.
The special angles that you need to know, with their sines, cosines, and tangents are:
When written in this way, the sines make a lovely pattern of $\sqrt1/2$, $\sqrt2/2$, $\sqrt3/2$, with the cosines in the opposite order. You can work out the tangents by dividing sine by cosine. (I’m using $\sqrt1/2$ to make the pattern clear, but we would of course use $1/2$ instead.)
Or if you want to use a calculator, you can learn to recognise $0.866\cdots$ as $\sqrt3/2$ and $0.707\cdots$ as $\sqrt2/2$, or you can get the exact value by squaring the answer, for example $\sin60^\circ$ will give $0.866\cdots$, and if you square this, you’ll get $3/4$, whose square root is $\sqrt3/2$.