Expert: Sherry Wallin - 3/28/2010

Question
Hello, I am having a difficult time trying to answer these questions:

A) 2sin^2-5sinx+2=0
B)3cos2x-5cosx-1=0
C)2sin^2x-1=0
D)1-cos2x-sinx=0
E)sin^2x+cos2x-cosx=0
F)tan^2x-(squareroot of 3)+tanx=0


Thanks

Answer
Cierra~
    It would be helpful if you would show me how you begin to do one of these problems so that I can help you figure out where you go wrong.
Since you did not give me further instructions I am assuming your instructions are for you to find solutions to the trigonometric equations.

Although many of these can be factored 'as is' sometimes it is easier to make substitutions, for example 2sin^2-5sinx+2=0 you can let sinx = u so that you now have 2u^2-5u+2= 0 ->(2u-1)(u-2) = 0 -> 2u-1=0 so 2u = 1 and u = 1/2. u-2=0 gives us u = 2. You need to go back and substitute for u in the original equation so you have sinx = 1/2 and sinx = 2. You can take the arcsin(sinx) = 1/2 or ask yourself what angle is the sin equal to 1/2? And you will know that the angle is 30 degrees but it is also 150 degrees because 30 degrees is the reference angle and because y = sin x is always positive in the first and second quadrants. sinx = 2 has no solution since the sin of any angle falls in the interval [-1,1]. Stated another way |sinx|<=1.

Math Prof