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# MEI C4 Question Help watch

1. I'm stuck on this question

i) Find the values of the acute angle A for which 5cosx-3sinx=√(34)cos(x+A) for all x.

ii) solve the equation 5cosx-3sinx=4 for 0°≤x≤360°

iii) solve the equation 5cos2x-3sin2x=4 for 0°≤x≤360°

So far I worked out
i) by having A =arcos 5/√(34)=30.96°
ii) cos(x+30.96)=4/√(34)
Arccos(4/√(34))=x+30.96
X=15.73

But the answers say there is another vaule for x, x=282.4° but I'm not sure how you get it. I though you have to add 180 or minus 15.73 from 270 or something like that but I just can't get to that answer

And because I can't do ii) I don't know what to do for iii)

Any help? Thanks

---Moved to Maths---
2. (Original post by Reags)
I'm stuck on this question

i) Find the values of the acute angle A for which 5cosx-3sinx=√(34)cos(x+A) for all x.

ii) solve the equation 5cosx-3sinx=4 for 0°≤x≤360°

iii) solve the equation 5cos2x-3sin2x=4 for 0°≤x≤360°

So far I worked out
i) by having A =arcos 5/√(34)=30.96°
ii) cos(x+30.96)=4/√(34)
Arccos(4/√(34))=x+30.96
X=15.73

But the answers say there is another vaule for x, x=282.4° but I'm not sure how you get it. I though you have to add 180 or minus 15.73 from 270 or something like that but I just can't get to that answer

And because I can't do ii) I don't know what to do for iii)

Any help? Thanks

---Moved to Maths---
you are right up to x + 30.96 = 46.686.

use cast diagram now to find another value of that equals

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