SOLUTION: Find all values of t in the interval [0,2π] if cot t-3tan t=0

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Question 334139: Find all values of t in the interval [0,2π] if cot t-3tan t=0
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of t in the interval [0,2π] if cot%28t%29-3%2Atan%28t%29=0

Cot%28t%29-3%2ATan%28t%29=0

Use the identity Tan%28theta%29=1%2FCot%28theta%29

Cot%28t%29-3%2A%281%2FCot%28t%29%29=0

Multiply through by Cot%28t%29

Cot%5E2%28t%29-3=0

Cot%5E2t=3

Use the principle of square roots:

Cot%28t%29=%22%22+%2B-+sqrt%283%29

The solutions are all angles with a reference angle of pi%2F6

pi%2F6, 5pi%2F6, 7pi%2F6, 11pi%2F6

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of t in the interval [0,2π] if cot t-3tan t=0
---------------
cot(t) - 3tan(t) = 0
Multiply by tan(t)
1 - 3tan^2 (t) = 0
3tan^2(t) = 1
tan^2(t) = 1/3
tan(t) = ± sqrt(3)/3
t = 30 degs, 210 degs
t = pi/6, 7pi/6 radians