Question 1160136
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Use the given information to determine the values of sin(2*theta)​, cos(2*theta), and tan(2*theta).
cos theta=8/17; The terminal side of theta lies in quadrant IV.
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        The solution in the post by @MowMow has two deficiencies.


        First, it is FATALLY incorrect.


        Second, in his post, the educational part of the solution disappeared in full.

        So, I came to provide a correct solution to this problem in the form as it should be 

        (as it is expected to be).


 
<pre>
Since  {{{cos(theta)}}} = 8/17  and angle {{{theta}}} is in quadrant IV,

    {{{sin(theta)}}} = {{{-sqrt(1-cos^2(theta))}}} = {{{-sqrt(1-(8/17)^2)}}} = {{{-sqrt((17^2-8^2)/17^2)}}} = 

                     = {{{-sqrt((289-64)/17^2)}}} = {{{-sqrt(225/17^2)}}} = {{{-15/17}}}.


Notice that we us sign  '-'  at the square root since angle {{{theta}}} is in quadrant IV, 
where 'sin' is negative.


Now  {{{sin(2*theta)}}} = {{{2*sin(theta)*cos(theta)}}} = {{{2*(-(15/17))*(8/17)}}} = {{{-240/289}}} = -0.8304.

     (compare this correct approximate value with incorrect value of 0.8304 in the post by @MowMow).



For  {{{cos(2*theta)}}},  use the formula

     {{{cos(2theta)}}} = {{{cos(theta + theta)}}} = {{{cos(theta)*cos(theta)-sin(theta)*sin(theta)}}} = 

                       = {{{cos^2(theta)-sin^2(theta)}}} = {{{(8/17)^2 - (-15/17)^2}}} = {{{64/289-225/289}}} =  {{{-161/289}}} = -0.5571.



For {{{tan(2*theta)}}},  use

     {{{tan(2*theta)}}} = {{{sin(2*theta)/cos(2*theta)}}} = {{{((-240/289))/((-161/289))}}} = {{{240/161}}} = 1.4907.

     (compare this correct approximate value with incorrect value of -1.4907 in the post by @MowMow).
</pre>

Solved, and you have clear instructions/guidance on how to do the solution.



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@MowMow, it is clear from your post, that you 


    &nbsp;&nbsp;&nbsp;&nbsp;- don't know right-angled triangles

    &nbsp;&nbsp;&nbsp;&nbsp;- don't know Pythagorean triangles

    &nbsp;&nbsp;&nbsp;&nbsp;- do not understand the meaning of this assignment

    &nbsp;&nbsp;&nbsp;&nbsp;- and do'n't know (have no idea) on how to solve it correctly.


I observed your contribution to the forum,


and with 179% confidence I can say that you have no necessary knowledge to be a Math tutor.


I ask you STOP posting to this forum.