Trigonometric Part of HSC 2016 Q 16 a) i) (1 Viewer)

frog1944

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Hi,

I was curious for Q 16 a) i), why does sin(theta)=sin(-alpha) mean that theta = - alpha? Why don't you have to consider it in terms of general solutions, with theta = 2*pi*k - (-1)^k alpha, and then some how work it out from there?

If -pi < x <= pi, -pi < y < pi, and sin(x) = 1/2 and sin(y) = -1/2, then couldn't x = pi/6, 5pi/6 and y = -pi/6, -5pi/6 . Then, couldn't x = pi/6 and y = -5pi/6, then x does not equal -y?

Thanks
 

dan964

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Substitute z and w into the equation given and take real and complex parts

(1)
(2)

Solutions to (2) are and The latter does not solve (1), as upon substitution gives 1=0, as leaving as the only valid solution
 
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frog1944

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Awesome! Thank you so much dan964 :) . I thought I was going crazy wondering why when only considering (2) theta could only equal - alpha.
 
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