SOLUTION: Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a comma-separated list.) (4 cot t)^2 = 48

Algebra ->  Trigonometry-basics -> SOLUTION: Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a comma-separated list.) (4 cot t)^2 = 48       Log On


   

Question 949907: Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a comma-separated list.)
(4 cot t)^2 = 48
Answer by lwsshak3(11628) About Me  (Show Source):
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Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a comma-separated list.)
(4 cot t)^2 = 48
take sqrt of both sides
4cot t=±√48=4±√3
cot t=(4±√3)/4
..
cot t=(4+√3)/4
t≈1.04, 4.18 (radians) (In quadrants I and III where cot>0)
..
cot t=(4-√3)/4
t≈1.94, 4.34 (radians) (In quadrants II and IV where cot<0)