A Level Maths Trig Question

https://www.quora.com/profile/Bravewarrior/p-164987414
Here is the question with its solution. I'm stuck on ii and I followed the route I highlighted in yellow on the mark scheme when I was solving this question. My problem is when I got to sin2theta=21/25, the inverse of sin(21/25) divided by 2 gives theta = 28.57
This is not one of the solutions and yet it clearly falls in the given range. Can someone please tell me where I went wrong and what i should've done? Thanks!

(edited 1 year ago)

Reply 1

Deniable

Yeah so what squaring does is that it introduces extra solutions, because pretend the 2 on the RHS of the equation was -2 instead, squaring would still produce a 4 on the RHS. For 2t, 0 <= 2t < 720, since sin2t = +ve, you'll have 4 solutions for 2t, hence 4 solutions for t, 2 of these solutions would produce a -2 when subbed back into the original equation. Whereas the other 2 would satisfy it.