C3 Trig (Rsinθ expansion) question maximum and minimum

You know the maximum value, right? So you set f(t) as the maximum value and solve for t between 0 and 24, and take the highest value of t.

As you can see from my workings this is what I have done. sin^-1(1)=90 and using my cast diagram this means I can only use '15t-26.6'=90. and this means t ends up being 7.77 as in my workings. I don't understand why they have made '15t-26.6'=270 in the markscheme as I dont see why this is allowed. And I do not understand where the 'mod' signs come into this answer either. Please could you point me in the right direction of where I am going wrong?

This is because of the modulus sign. since you have 1=|x|, x could be 1 or -1, right? Therefore sin(15t-26.6) could be 1 or -1, hence the max value of t occuring when sin(15t-26.6) = -1

Ok thank you so much I understand this now. Because sin^-1(-1) = -90 this allows it to equal 270 (cos and tan sectors). And then then add 26.6 divide by 15 and you get the anwer they were asking for. Thank for your help again.