Question

tan2θ−√3tanθ=0

Find all solutions in the interval [0,360°)

Answer 1

thanks for helping

Answer 2

tan(2x) = 2tanx/(1- (tanx)^2)

tan2x - sqrt(3)tanx = 2tanx/(1- (tanx)^2) - sqrt(3)tanx = 0

2tanx - (1- (tanx)^2)) *[ sqrt(3)tanx] = 0

2-1+ sqrt(3) (tanx)^2 = 0

now solve for tanx!

Answer 3

so is it tanx=sqrt (1/1+sqrt3)??? then how do i convert it to intervals of [0,360degrees)?

Answer 4

thanks for coming back!

Answer 5

actually, it's tanx = sqrt(1/sqrt3)

Answer 6

so... actually tanx is equal to plus or minus sqrt(1/sqrt3)..


Positive right hand side: Take the inverse tangent to get 37.22 degrees... Now the only other value which equals sqrt(1/sqrt3) is 180 degrees plus that

Negative right hand side: Take the inverse tangent to get 322.77 degress... The only other tan of a value to equal -sqrt(1/sqrt3) is 180 degrees less than that!

Answer 7

so, is the solution set: 37, 143, 217 322) ????

Answer 8

yup! Good job!