Vectors

Could anyone explain why the sin and cos is the other way around?

Where has that angle marked "60" come from in the diagram - is that your annotation? Note that 240 = 180 + 60 so the line OA should be 60 degrees below the x-axis, not 60 degrees with the y-axis!

But measuring from the y-axis clockwise that would be 240? (That is my annotation)

Bearings are measured clockwise from N (i.e. +ve y-axis) so that may be where confusion arises.

Why are you measuring anything from the y-axis clockwise? Angles start at 0 for points on the x axis, a +ve rotation of 90 degrees takes you to the +ve y-axis, a further rotation of +90 degrees takes you onto the -ve x-axis and you want to go on a further 60 degrees beyond that to get to 240 degrees!

Do you always Start from the x axis unless told otherwise?

Certainly - that's the whole basis of how trig functions are used in conjunction with (x, y) coordinates and so-called circular measure - the usual parameterisation of the unit circle is by using x= cos t, y = sin t where t is measured in a positive direction from the positive x-axis..

Are you new to this topic, or were you just confused by the wording of the question? Have you not come across the CAST diagram covering the signs of the respective trig functions in each quarter of the circle?

I don’t know if I’m new to this topic but this is my first time doing a question like this. I’ve never seen the CAST diagram

OK fair enough. Is this question from an exam paper or part of a text book exercise? If it;s from a book I'd expect them to introduce the topic by giving you a few practice examples for small angles first e.g. OA has magnitude 5 and direction 20 degrees, so you get used to working out x = 5cos20, y = 5sin20 to plot a simple point in the 1st quadrant etc

It’s just from a paper, do you know what this topic is called or is it just the CAST diagram?

It's not the CAST diagram per se - I was just quoting that because I thought it might be something you were more familiar with!

I'd say it was just basic vectors - the important concept being that if you have a direction vector starting from the origin O then the angle given is from the positive x-axis, NOT from the vertical as it is when you do bearings at GCSE. Maybe have a glance through some introductory vectors questions in your textbook to see if you can find similar examples