Hello misspalmer

Welcome to Math Help Forum!First, I assume that the hyphens at the left-hand end of each equation are not minus signs. You do need to be careful in writing down the questions!

Then you need to know how sine and cosine behave between and . So take a look at the diagram I've attached.

You'll see that goes from to as goes from to . Then, in a symmetrical way, it goes back down to as goes from to .

So, for any number between and , there will be two angles whose sine is this number: one between and and one between and . But if the number lies outside the range to , there won't be any angles between and having this number as their sine.

On the other hand, starts at and goes down to as goes from to . Then it continues down to as goes from to .

So no value of is repeated as takes values between and . So none of the equations involving cosine will have two answers.

If you apply the rules I've just given you, it should be pretty clear what the answers are. For instance, the first equation, , will have two solutions, but the second, , won't.

Can you do the rest of them now?

Grandad