csc x tan x=2√3/3
(1/sinx)(sinx/cosx) = 2√3/3
1/cosx = 2√3/3
cosx = 3/2√3
= 3/2√3 * √3/√3
= √3/2
from my 30-60-90° triangle I know that cos 30° = √3/2
since the cosine is positive in quad I and IV
x = 30° or x = 330°
in radians: x = π/6, 11π/6
What are ALL the solutions of the equation csc x tan x=2√3/3 on the interval [0,2π)? List all the correct solutions from the box.
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π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π
7π/6 5π/4 4π/3 3π/2 5π/3 7π/4 11π/6
1 answer
2 answers