SOLUTION: given that {{{cos(x) = 3/5}}}, {{{3pi/2 < x < 2pi}}} find {{{cos(x/2)}}}, {{{sin(x/2)}}}. {{{tan(x/2)}}}

Question 921668: given that , find
, .
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

,  find 
, , and .

Since , dividing the three sides of the inequality by 2,

, which tells us that  is in quadrant II

To find  will need the half-angle formulas:



But since  is in quadrant II, its cosine is negative, so we
will only use the negative sign:

 

To simplify , multiply top and bottom by 5, 

So 

---------------------

To find  will need the half-angle formulas:



But since  is in quadrant II, its sine is positive, so we
will only use the positive sign:

 

To simplify , multiply top and bottom by 5, 

So 

-------------------------

To find  there are several half-angle identities we could
use.

 

However I think since I already have the sine and cosine of ,
I'll use the quotient identity:



Edwin

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