SOLUTION: Use the given information to find {{{sin 2(phi)}}}, {{{cos 2(phi)}}}, {{{tan 2(phi)}}}. 1. {{{tan(phi)=1/2}}}, {{{pi < phi <= (3pi/2)}}} 2. {{{sec(phi)=-5/2}}},{{{pi/2 < phi

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Question 142454: Use the given information to find , , .
1. ,
2. ,
3. ,
Any help is greatly appreciated.
Thanks,
Justin

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Use the given information to find , , .

Formulas needed are

 



1. ,  

That's the THIRD quadrant.

Draw a picture of angle theta in the third quadrant

Since  

If theta were in the first quadrant, we'd let the 
numerator of  be y and the denominator of 
 be x.  But since theta is in the third 
quadrant, we have to make x and y both negative.  
So take y, the opposite, as the negative of the 
numerator, -1, and take x to be the negative of 
the denominator, -2. 

So plot the point (-2,-1) in the third quadrant and 
draw a radius to it and draw a perpendicular up to 
the x-axis, forming a right triangle:



Next we need to find r, the hypotenuse. We use the
Pythagorean theorem:











So we label that:



Now we have ,,
And so 



Substituting in

 



Substituting in









Substituting those values in:






If I have time I'll come back and do the others.

Edwin






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