I would "solve" the equation this way:
3 cot^2 x -1 = 0
cot^2 x = 1/3
tan^2 x = 3
tan x = ±√3
so x is in any of the 4 quadrants,
x = 60° , 180°-60° , 180°+60° , 360°-60°
= 60° , 120° , 240° or 300°
in radians: π/3, 2π/3, 4π/3, 5π/3
location of a unit circle:
(±1 , ±√3)
the period of tanx = 180°
notice the diffence between the 1st and 3rd solution is 180°, and the difference between the 2nd and 4th is 180°
so a general solution could be written as
(60° + 180k°) , (120° + 180k°)
I will let you change those to radians if needed.
for the #2, I will start you off
sin^2 x = 3cos^2 x
sin^2 x/cos^2 z = 3
tan^2 x = 3
tanx = ± √3
mmmhhh , looks familiar
Hi! Can someone help me with these? I just learned about them yesterday but I'm really confused. All my teacher wants me to do is solve each equation and that's all the directions she gave. Thanks so much!
1.) 3cot^2 x-1=0
Location on Unit Circle:
Period:
General Solution:
2.) sin^2x=3cos^2x
Location on Unit Circle:
Period:
General Solution:
1 answer
1 answer