Question 1042537
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If sin (theta) =  2 over 7 and tan (theta) > 0, what is the value of cos (theta)?

I need to show work
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<pre>
You are given {{{sin(theta)}}} = {{{2/7}}}.


Then {{{cos(theta)}}} = {{{sqrt(1-sin^2(theta))}}} = {{{sqrt(1-(2/7)^2)}}} = {{{sqrt(1 - 4/49)}}} = {{{sqrt((49-4)/49)}}} = {{{sqrt(45/49)}}} = {{{(3*sqrt(5))/7}}}.


Since {{{sin(theta)}}} is positive and {{{tan(theta)}}} is positive (given !), the angle {{{theta}}} is in the first quadrant.


Since {{{theta}}} is in QI, the sign at the square root is positive.

<U>Answer</U>.  {{{sin(theta)}}} = {{{(3*sqrt(5))/7}}}.
</pre>

Solved.