Double Angle Identites (Trig Ratios)

Dhkajsd

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Jul 20, 2019
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Q. from textbook :

DC4328EB-AC17-48ED-A807-84D2B06D8C7C.jpeg

Working:

FA9C1A13-4E17-481F-BE9D-200C93538126.jpeg

Thanks a lot for any assistance
 

MarkFL

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Hello, and welcome to FMH! :)

Your working would be correct if the angle \(A\) were a first quadrant angle. But, it's a second quadrant angle. So, what must the sign of the cosine function there be?
 

pka

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Given that \(\displaystyle 90o\le A\le 180^o\) means that \(\displaystyle 180^o\le 2A \le 360^o\) is in either the third or fourth quadrant.
So then \(\displaystyle -1\le\sin(2A)\le 0.\)


 

Dhkajsd

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Jul 20, 2019
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Than
Hello, and welcome to FMH! :)

Your working would be correct if the angle \(A\) were a first quadrant angle. But, it's a second quadrant angle. So, what must the sign of the cosine function there be?
Thank you, didn’t realise it was so simple :) it must be negative
 
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