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Use the Quadratic Formula to solve the equation in the interval [0, 2pi). Then use a graphing utility to approximate the angle x.
15 sin^2x - 22 sinx + 8 = 0
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Let u = sin(x) be the new variable.
Then your equation takes the form
= .
Solve it for "u" using the quadratic formula:
= = = ,
= = and = = .
Then you have two equations:
1) sin(x) = ---> x = arcsin(4/5), and
2) sin(x) = ---> x = arcsin(2/3).
Next use your calculator.
The way of introducing new variable is the standard method for solving equations like this one.