1: That just means sin(theta) = opposite/hypotenuse
2. For that one (which is a bit dodgier), you're basically referring to
this diagram. Ignore the stuff about versin and exsec.
3. y=mx+b
m=tan(theta)
4. Basically what you said
5. pi radians = 180 degrees
6. The formula for the area of a sector is \(A=\frac12r^2\theta\) where theta is in radians
For a minor segment it's \(A=\frac12r^2(\theta-\sin\theta)\)
7. Same as 1.2.2, just with radians and not degrees
8. There are tricks for memorising exact values between 0 and pi/2. If you want I can provide that later. The dot point is self explanatory though
9. I think that just means "any" domain. 'Extended domain' is not a term in the world of mathematics. Important thing is you can recognise the graph.
For 10-12, I recommend you experiment using
GeoGebra. Just submit the graphs in and see what happens. (Desmos also works)
13. I think you forgot bracketing. But basically \(\sin \left(x+\frac\pi2\right)=\cos x \) is an identity and if you graph it, you should be able to see why.
14. There are tons of identities. Idk which are in your curriculum.
15. Practical problems = you're given a scenario and you have to do it. It's like some of the angle of elevation questions and those really wordy problems you've asked Jamon