What is the solution to 11 = x – 4?
2 answers:
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The solutions appear to be {π/2, 2π/3, 4π/3}.
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
see the attached figure to better understand the problem
Let
2L---------> lenght side of hexagon
we know that
in one of those triangles
sin 30=1/2
sin 30=L/hypotenuse
solve for L
L=hypotenuse*sin 30-------->L=( 1 8 √ 3 )*(1 /2)------> L=9√3 units
Find the perimeter
perimeter=(2L)*6--------> L*12-------> Perimeter=9√3*12--------->108√3 units
therefore
the answer is
the perimeter of the regular hexagon is 108√3 units
