Answer:
1. 30
2. 150
Step-by-step explanation:
[tex]3tan^2(x)-1 =0[/tex]
Lets assume tan(x) = u
[tex]3u^2(x)-1 =0[/tex]
Now we solve for 'u'
add 1 on both sides
[tex]3u^2(x) =1[/tex], divide both sides by 3
[tex]u^2 = \frac{1}{3}[/tex]
Take square root on both sides
[tex]u = +-\frac{1}{\sqrt{3} }[/tex]
We replace tan(x) for 'u'
[tex]tan(x) = +-\frac{1}{\sqrt{3} }[/tex]
x = 30 because [tex]tan(30) =+\frac{1}{\sqrt{3} }[/tex] in first quadrant
x = 30 (tan is positive in first quadrant)
[tex]tan(x) =-\frac{1}{\sqrt{3} }[/tex]
x = 150 because [tex]tan(150) =-\frac{1}{\sqrt{3} }[/tex] in second quadrant
tan is negative in second quadrant
Answers:
First quadrant: 30°
Second quadrant: 150°
Explanation:
I got it correct in my test :)
