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Single trig Functions

I need help solving this equation

it is 5sin(x/2)-12cos(x/2)=-6.5 I know you have to make it into a single trig function but i dont really know what to do

here is what I did first Rsin((x/2)+a)
R=root of 5^2+12^2=13
then
R(sin(x/2)cosa+cos(x/2)sina)
Rsina=-12
Rcosa=5
a=arctan-12/5 a = -67.4
so this gives me 13sin((x/2)-67.4)=-6.5 and then solved which gave me
(x/2) -67.4=-30 but the x value I get is 18.7 but the book says -168.4 or something
someone please tell me where I went wrong. And how I can do this question

Reply 1

TenOfThem

Original post by Iowan

(x/2) -67.4=-30 but the x value I get is 18.7 but the book says -168.4 or something
someone please tell me where I went wrong. And how I can do this question

I do not see how you get 18.7 from that unless you divided by 2 when you should have multiplied by 2.

As with all trig equations, there are infinite possible answers, were you given a range for the answer?