Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) − 9 = 0

1 Answer
Natalie
Jan 15, 2018

#x=pi/3, (5pi)/3#

Explanation:

First isolate X:
#18cosx-9=0#
#18cosx=9#
#cosx=9/18#
#cosx=1/2#
Now that we know that Cosine of X =#1/2#, we can use the unit circle to find which angles satisty the equation.
Points on the unit circle are #(cos, sin)#, so any point on the unit circle that has an x value of #1/2# is a solution. The angles that satisfy this condition are #pi/3# and #(5pi)/3#.

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