Pleaseee, what is the answer to the last part

Have you had a go at the last part? That's the advice given in the original response, and I'm reluctant to deviate from it because I think it's 100% correct - you should have a go first.

Hi everyone! Just wondering if someone could let me know how they would have thought about the question below, needing to find tan from sin. I understand how they got the answer but didn't think to simplify the denominator by factorising. What would you look for/what hints would you take from the question to do this?

Thanks!

This sort of factorisation should be relatively standard as you do look into completing the square when you study solutions to quadratics. It's in a different form so it may not be immediately obvious, but you should be on the lookout for things like this regardless. More of a practice thing to get your eye in on these sorts of tricks. It's not strictly necessary to employ this trick in this particular instance, in any case.

When I looked at the solutions for the question below it said that you should dilate and then translate which is weird because aren't you supposed to do what is in the parenthesis first? Is this a misconception?

You're thinking of computing equations. SnekiSnek is correct

Someone please help I don't think I know how to use a calculator

\(z = \frac{x - \mu}{\sigma}\). If the numbers in the table were all correct, \(\mu, \sigma\) would be equal in a system of linear equations. Solve two simultaneously to find values of \(\mu, \sigma\) then sub into the other result to see what adjustment needs to be made (and if it matches one of the other options given).

I'm not giving you the answer because I don't really see an attempt ('someone please help' is not really helpful to me because I want to help you target the bits you're struggling with, I'm only able to give you general advice in this case).

In future, please add more working and refrain from doing a double post, let alone a quadruple