SOLUTION: If sinx = 15/17 an X is in quadrant 1, find the exact values of sin X/2 and cos x/2

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Question 1081528: If sinx = 15/17 an X is in quadrant 1, find the exact values of sin X/2 and cos x/2
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Note: In the figure b = |BC|, h=|BD|
—> set b=15 and c=17
Solve for a:
—
Because x is bisected: <<—<<< angle bisector theorem
—> —>
—
We need 'd':

Finally, ready to solve:


—
I will leave it to you to find cos(x/2). You can use and plug in a & d (easiest way).

Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
If sinx = 15/17 an X is in quadrant 1, find the exact values of sin X/2 and cos x/2
~~~~~~~~~~~~~~~

The standard technique for solving such problems is THIS: 

1.  cos(x) =  =  =  =  =  = 


    notice sqrt is taken with the sign "+" since the angle "x" is in Q1 by the condition.



2.  Now   =    (apply the Trigonometry formula for half-argument)

         =  =  =  =  =  = .

    Again, the sign is "+" at the sqrt since x/2 is in Q1 together with x.



3.  Next   =    (apply the Trigonometry formula for half-argument)

         =  =  =  =  =  = .

    Again, the sign is "+" at the sqrt since x/2 is in Q1 together with x.

Solved. 

For half-argument formulas of Trigonometry see the lessons
    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS
    - Trigonometric functions of half argument
in this site.


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