You can put this solution on YOUR website! Solve for (0<=x<=360)
sin2x-cosx=-1+2sinx
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sin(2x)-cos(x)=-1+2sin(x)
2sin(x)cos(x) - cos(x) = -1 + 2sin(x)
cos*(2sin - 1) = -1 + 2sin = -(2sin - 1)
cos(x) = -1
x = 180 degs
Step by step
sin(2x) - cos(x) = -1 + 2sin(x)
2sin(x)cos(x) - cos(x) = -1 + 2sin(x)
cos(x)*(2sin(x) - 1) = -1 + 2sin(x)
cos(x)*(2sin(x) - 1) - (-1 + 2sin(x)) = 0
(cos(x)-1)*(2sin(x)-1) = 0
Case 1: cos(x)-1 = 0 ---> cos(x) = 1 ---> x = 0.
Case 2: 2sin(x) -1 = 0 ---> 2sin(x) = 1 ---> sin(x) = 1/2 ---> x = 30 degrees or x = 150 degrees.
ANSWER. There are 3 (three) solutions: x= 0 degrees; x = 30 degrees and x= 150 degrees.
Solved (correctly).
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For this problem, and for many other problems, if the restriction for the argument
is for one period, it is usually (ALWAYS) should be written in the form 0 <= x < 360
and NOT in the form 0 <= x <= 360, because 0 and 360 represents
the same geometric angle (although different numbers).
This small detail - how do you write this restriction - in correct form 0 <= x < 360
or in incorrect form 0 <= x <= 360, makes it clear from the first glance
whether you know the subject and are familiar with standard mathematical notations - or not.
