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Math Help - quite urgent..exam in 2 days!!

  1. #1
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    Unhappy quite urgent..exam in 2 days!!

    just doing some past papers and there is a type of question that I can't understand..ever!

    for example:
    solve the equation: sin(θ - 30) = 0.7 in the interval 0≤ θ ≤ 360
    solve the equation: cosx=0.3 in the interval 0 ≤ x ≤ 2π
    can anyone help me please??
    thank you!

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  2. #2
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    Basically, you are asked to solve for the variable. For example, your first question:

    sin(\theta-30^\circ) = 0.7
    \theta - 30^\circ = arcsin(0.7)
     \theta = arcsin(0.7)+30^\circ

    Now punch that through your calculator. arcsin is more often this button:  sin^{-1}

    Remember that there are two quadrants in the unit circle where sin is positive, so in a complete circle (360 degrees), there are two solutions to this problem.

    Now do the second one in the same way
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  3. #3
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    how do I relate this to the interval?
    I know it's something to do with the graphs for sin and cos but how do I work out the answers for the interval given?
    thanks
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  4. #4
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    One Method:
    Use the unit circle. One revolution of the circle is 360 degrees (or 2pi). Sine is positive in the 1st and 2nd quadrants. So the solutions to consider are is  \theta and  180-\theta.
    __________________________________________________ _____________
    If you are unfamiliar with the unit circle, just use the general solutions for the sine:
    Having found the basic value of  \theta (which is  arcsin(0.7)+30^\circ), substitute it into the general equation for the sin.

     x = 180^\circ n + (-1)^n  (\theta)
    where x is a solution, and n is an integer larger or equal to zero (0,1,2,3...)

    Substitute n =0 to get the first solution, n= 1 for the second, n= 2 for the third and so on...

    You'll find that after n = 1, the angles will become larger than 360, and thus not within your parameters. That leavs you with two solutions.
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