A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find all solutions in the interval [0, 2π). 4 sin2x - 4 sin x + 1 = 0
Solution:
It is given that, equation:
4 sin2x - 4 sin x + 1 = 0,
We can say sin x = a, then the equation becomes:
4a2 - 4a + 1 = 0
By dividing 4, we get,
a2 - a + 1/4
So, (a - 1/2) (a - 1/2) = 0
a = 1/2
Then,
sin x = 1/2
Because the interval between 0 - 2π and positive sin values are in quadrants 1 and 2 so the x values that meet are 30° and 150° or π/6 and 5/6 π.
Therefore, 30° and 150° or π/6 and 5/6 π are the solutions.
Find all solutions in the interval [0, 2π). 4 sin2x - 4 sin x + 1 = 0
Summary:
All solutions in the interval [0, 2π) 4 sin2x - 4 sin x + 1 = 0 are 30° and 150° or π/6 and 5/6 π.
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