Question 1099998
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<pre>
Find the exact value of the expression or state that it does not exist.
cos(sin^-1 ( sqrt(3)/ 5))



a.  In the function y=sin^-1(x), the expression sin^-1 x is defined as an angle in what interval? 


        [{{{-pi/2}}}, {{{pi/2}}}], by the definition of the function arcsin(x)  (which is exactly the same as  sin^(-1) (x) )



b.  Where does the terminal side of sin^-1 (sqrt(3)/5) lie? 


        In the first quadrant.



c.  Determine the value of cos(sin^-1 ( sqrt(3)/ 5)). 


        You are given that  {{{sin(alpha)}}} = {{{sqrt(3)/5}}}.


        Then {{{cos(alpha)}}} = {{{sqrt(1-sin^2(alpha))}}} = {{{sqrt(1 - (sqrt(3)/5)^2)}}} = {{{sqrt(1 - 3/25)}}} = {{{sqrt((25-3)/25)}}} = {{{sqrt(22/25)}}} = {{{sqrt(22)/5}}}.
</pre>

Solved.



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To see more solved problems of this kind,  look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Calculating-trigonometric-functions-of-angles.lesson>Calculating trigonometric functions of angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Selected-problems-from-the-archive-on-calculating-trig-functions-of-angles.lesson>Advanced problems on calculating trigonometric functions of angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Evaluating-trigonometric-expressions.lesson>Evaluating trigonometric expressions</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Trigonometry: Solved problems</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.