The equation becomes

Subtract 2 from both sides.

Multiply each term by negative 1.

Substitute

That's a quadratic polynomial.

so x=1

Arcsin (1) = 90 degrees. That's only one possible answer, because sin repeats every 2*pi radians (360 degrees). The complete answer is pi + 2*pi*n radians, or 90 + 360n degrees.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

Answer by Leaf W.(135)   (Show Source): You can put this solution on YOUR website!

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Since (a fundamental trigonometric identity), you can change this to using basic algebra subtraction on both sides and substitute this into your equation for .
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Move everything to the right side:
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Factor:
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Solve for : ==>
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Now you have to think: for what angles is the sine equal to 1? Well, for . However, it is also 1 at every complete revolution (every from -- that is, , where "n" is an integer {think , , etc.}). Therefore, the solution to the equation is .
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IF you have a domain restriction in the problem, only include solutions that are within the domain. For example, if you have a restriction of , then your solution would be only because that is the only solution in that is between 0 and .
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I hope this helped! Good luck!