Question 1081528
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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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The standard technique for solving such problems is THIS:


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1.  cos(x) = {{{sqrt(1-sin^2(x))}}} = {{{sqrt(1-(15/17)^2)}}} = {{{sqrt(1 - 225/289)}}} = {{{sqrt((289-225)/289)}}} = {{{sqrt(64/289)}}} = {{{8/17}}}


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



2.  Now  {{{sin(x/2)}}} =    (apply the Trigonometry formula for half-argument)

         = {{{sqrt((1-cos(x))/2)}}} = {{{sqrt((1-8/17)/2)}}} = {{{sqrt((17-8)/(17*2))}}} = {{{sqrt(9/34)}}} = {{{3/sqrt(34)}}} = {{{(3*sqrt(34))/34}}}.

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



3.  Next  {{{cos(x/2)}}} =    (apply the Trigonometry formula for half-argument)

         = {{{sqrt((1+cos(x))/2)}}} = {{{sqrt((1+8/17)/2)}}} = {{{sqrt((17+8)/(17*2))}}} = {{{sqrt(25/34)}}} = {{{5/sqrt(34)}}} = {{{(5*sqrt(34))/34}}}.

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


<pre>
For half-argument formulas of Trigonometry see the lessons
    - <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Compendium-of-Trigonometry-Formulas.lesson>FORMULAS FOR TRIGONOMETRIC FUNCTIONS</A>
    - <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-half-argument.lesson>Trigonometric functions of half argument</A>
in this site.
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