trigonometry help mark scheme confusing

will post below

I managed to get the first two marks but the next two didn't make sense to me. I got sin alpha equals 4/9 but I don't know how we jumped from that to cos alpha equals root 65 over 9. Can someone explain?

Original post by someguy22

you can construct a right angled triangle where two of the sides are 4 and 9.

then you can work out the third side using a well known theorem.

then you can express the cosine as a fraction using two of the sides.

Reply 3

tonyiptony

Another way if you are allergic to drawing right-angled triangles:

You can use the Pythagorean identity - sin^2(x) + cos^2(x) = 1 - then plug-and-chug. That said, beware of signs.