Answer:
1.x = pi/3 or 4pi/3
2. x = -pi/6 +2pi*n or 5pi/6 + 2pi *n where n is an integer
Step-by-step explanation:
1. sqrt(3) tan x = 3
Divide each side by sqrt(3)
sqrt(3)/sqrt(3) tan x = 3/sqrt(3)
tan x = sqrt(3) * sqrt(3)/sqrt(3)
tan x = sqrt(3)
Take the inverse of each side
arctan (tanx) = arctan (sqrt(3))
x = arctan (sqrt(3))
x =pi/3 or - 2pi/3
Since the domain is between 0 and 2pi, add 2pi to - 2pi/3 since the trig functions are circular
x = pi/3 or -2pi/3 + 6pi/3
x = pi/3 or 4pi/3
2. 3 tan x = -sqrt(3)
Divide each side by 3
3/3 tan x = -sqrt(3)/3
tan x = -sqrt(3)/3
Take the arctan of each side
arctan (tan x) = arctan ( -sqrt(3)/3)
x = arctan ( -sqrt(3)/3)
x =-pi/6 or 5pi/6
We want all values for x so add 2pi*n to each value where n is an integer
x = -pi/6 +2pi*n or 5pi/6 + 2pi *n where n is an integer
