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# C4 problem Where am I going wrong? watch

1. This is a composite angle formula question, and I keep getting the answer wrong! Can anyone tell me what I'm doing wrong/how to fix it

sin(45-X) = CosX

Sin45CosX-Cos45SinX=CosX

Change into trig ratio

sqrt2/2CosX - sqrt2/2sinX=CosX

Divide through by Cosx

sqrt2/2 -sqrt2/2.tanX =1

sqrt2/2(1-tanx)=1

1-tanx = 2/sqrt2

tanx= 1-2/sqrt2

x=-22.5

but this is not the correct answer, the correct answer is supposed to be 157.5???
2. Tanx = 1 - 2/sqrt2 (you rearranged it wrong )
3. too slow ...
this by the way can be done very quickly without any compound angles or a calculator!
4. (Original post by PS4)
Tanx = 1 - 2/sqrt2 (you rearranged it wrong )
oh silly me, i corrected it! thanks!

however, that rearrangement gives me -22.5? which still isn't right!
5. (Original post by KateAteKarrots)
oh silly me, i corrected it! thanks!

however, that rearrangement gives me -22.5? which still isn't right!
]

never mind, i understand what i did now! i need to use cast! thanks so much for help
6. (Original post by TeeEm)
too slow ...
this by the way can be done very quickly without any compound angles or a calculator!
?
7. (Original post by KateAteKarrots)
]

never mind, i understand what i did now! i need to use cast! thanks so much for help
Yes, use CAST. I guess you were given a range in which to find the solutions? If so, use CAST to guide you, or draw out the periodic graphs of the appropriate functions to make it clear where the solutions will lie.
8. (Original post by atsruser)
?
I will post it for interest sake to others ....
9. (Original post by atsruser)
?
(Original post by TeeEm)
I will post it for interest sake to others ....
10. (Original post by TeeEm)
Of course!! Don't know how I missed that. Still, my suggestion works too...

#GoesAwayToHide
11. (Original post by TeeEm)
Even easier:
12. (Original post by atsruser)
Even easier:
viable variations ...

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Updated: February 1, 2016
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