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

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(32388) (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.
RELATED QUESTIONS
Find all values of x in the interval [0, 2pi] that satisfy the equation. 4 cos(x) - 2 =... (answered by lwsshak3)

Find all solutions in the interval [0, 2pi) Cos^2 (x/2) = cos^2... (answered by lwsshak3)

find all values x over the interval (0, 2pi), for the equation... (answered by stanbon)

Find all values of x in the interval (0, 2pi) that satisfy the condition: ((csc^2)x)-1=4 (answered by lwsshak3)

Find all solutions of the equation in the interval [0, 2pi).... (answered by Alan3354)

Find all solutions of each of the equations in the interval (0, 2pi) cos(x- pi/2) +... (answered by lwsshak3)

Find all values of x in the interval [0, 2π] that satisfy the equation (sin x) *... (answered by lwsshak3)

find all solution of equation for the given interval 3sin^2(x)-cos^2(x)=0 (answered by stanbon)

find all solution of equation for the given interval 3sin^2(x)-cos^2(x)=0 (answered by lwsshak3)