Question 1038839
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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

{{{15u^2 - 22u + 8}}} = {{{0}}}.

Solve it for  "u"  using the quadratic formula:

{{{u[1,2]}}} = {{{(22 +- sqrt(22^2-4*15*8))/30}}} = {{{(22 +- sqrt(4))/30}}} = {{{(22 +- 2)/30}}},

{{{u[1]}}} = {{{24/30}}} = {{{4/5}}}  and  {{{u[2]}}} = {{{20/30}}} = {{{2/3}}}.

Then you have two equations:

1) sin(x) = {{{4/5}}} --->  x = arcsin(4/5),  and

2) sin(x) = {{{2/3}}} --->  x = arcsin(2/3).

Next use your calculator.


The way of introducing new variable is the standard method for solving equations like this one.
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