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
Jan 15, 2018

x=pi/3, (5pi)/3x=π3,5π3

Explanation:

First isolate X:
18cosx-9=018cosx9=0
18cosx=918cosx=9
cosx=9/18cosx=918
cosx=1/2cosx=12
Now that we know that Cosine of X =1/212, we can use the unit circle to find which angles satisty the equation.
Points on the unit circle are (cos, sin)(cos,sin), so any point on the unit circle that has an x value of 1/212 is a solution. The angles that satisfy this condition are pi/3π3 and (5pi)/35π3.