How many solutions does the nonlinear system of equations graphed below have?
2 answers:
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Answer:
<h3><em>π/4 and 3π/4</em></h3>Step-by-step explanation:
Given the equation , we are to find all the values of x in the interval [0, 2π] that satisfies the equation.
Simplifying the equation:
Square both sides of the equation;
The general formula for sin(x) is x = nπ + (-1)ⁿ∝ where n = 0, 1, 2, 3...
Since ∝ = 45° = π/4.
x = nπ + (-1)ⁿπ/4
when n = 1
x = π + (-1)¹π/4
x = π - π/4
x = 3π/4
<em>Hence the values of x within the given interval are π/4 and 3π/4</em>