# SOLUTION: Find all values of "x" within the interval [0,2pi) for the equation: cos(x/2)= {{{ sqrt(2) }}}/2

Algebra ->  Trigonometry-basics -> SOLUTION: Find all values of "x" within the interval [0,2pi) for the equation: cos(x/2)= {{{ sqrt(2) }}}/2       Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Trigonometry-basics Question 106799This question is from textbook Precalculus with limits : Find all values of "x" within the interval [0,2pi) for the equation: cos(x/2)= /2 This question is from textbook Precalculus with limits Answer by Fombitz(13828)   (Show Source): You can put this solution on YOUR website!Since, You know from the relationship, As you can see on the unit circle, there are two angles (A and -A) that solve the equation, You can determine A several ways. Two ways are using the inverse trigonometric functions and geometrically. Using inverse trig, the only angle that has equal sine and cosine is 45 degrees, or Geometrically, the triangle with A as one angle is a right tringle. It is also an right, isoceles triangle with a hypotneuse of 1 and sides of Therefore A+A=90 or A=45.