SOLUTION: determine ALL the exact roots of the equation {{{4 sin^2x-3=0}}} by solving in an algebraic manner for the domain 0 degrees (less than or equal to)X(less than or equal to)360 degre

Algebra ->  Trigonometry-basics -> SOLUTION: determine ALL the exact roots of the equation {{{4 sin^2x-3=0}}} by solving in an algebraic manner for the domain 0 degrees (less than or equal to)X(less than or equal to)360 degre      Log On


   

Question 61261: determine ALL the exact roots of the equation 4+sin%5E2x-3=0 by solving in an algebraic manner for the domain 0 degrees (less than or equal to)X(less than or equal to)360 degrees.
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Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
4+sin%5E2x-3=0 Add 3 to both sides
4+sin%5E2x=3 Divide both sides by 4
1+sin%5E2x=3%2F4 I had to put the 1 in the front to get this to display properly but it is not needed in the written answer.
Find the square root of both sides. Remember there is both a positive and a negative root.
sinx=sqrt%283%29%2F2 or sinx=-sqrt%283%29%2F2
ie x could be 60, 120, 240 or 300 degrees.