cos(3x)=-1 (pre-cal/trig help?)?
Trig/pre-cal problem.
Part I: Using an appropriate inverse trig expression, write an equation that defines the value of 3x. (Is it Arccos(-1)?)
Part II: Solve this equation to find all possible values of the angle 3x.
Part III: Use algebra to find all values of x between 0 and 2pi that satisfy this equation.
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Your answer to Part I is correct 3x=Arccos(-1)
Part II: You have to ask yourself - At what angle is the value of cos = -1... cos is -1 at 180 degrees or pi radians.
Part III: The rest is fairly simple...change the equation to something more manageable to solve for x:
3x = 180 therefore x = 60 degrees
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cos (3x) = - 1
(1) 3x = cos^(- 1) (- 1) (read as cos inverse - 1 )
= Arc cos (- 1)
(2) 3x = 2nπ ± π , where n = 0 or any integer.
(3) x = π/3, π, 5π / 3