SOLUTION: 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

Algebra ->  Trigonometry-basics -> SOLUTION: 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       Log On


   



Question 1099998: 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?
b. Where does the terminal side of sin^-1 (sqrt(3)/5) lie?
c. Determine the value of cos(sin^-1 ( sqrt(3)/ 5)).

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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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%2F2, pi%2F2], 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%28alpha%29 = sqrt%283%29%2F5.


        Then cos%28alpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281+-+%28sqrt%283%29%2F5%29%5E2%29 = sqrt%281+-+3%2F25%29 = sqrt%28%2825-3%29%2F25%29 = sqrt%2822%2F25%29 = sqrt%2822%29%2F5.

Solved.


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To see more solved problems of this kind, look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Trigonometry: Solved problems".


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.