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Math Help - Trig. All solutions?

  1. #1
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    Trig. All solutions?

    how do i find out all the solutions for a trig question other than looking at a graph?

    you can use an example like sinx=0.5 ; cosx=0.5 ; tanx =0.5

    from -360<x<360.

    thanks for your help!
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  2. #2
    Senior Member apcalculus's Avatar
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    Need to get familiar with the unit circle.

    For example:
    From 0 to 2pi, there are two angles whose sine is 0.5; they occur in the first and second quadrants. Because you're going from -2pi to 2pi, that means the equation will have four solutions.
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  3. #3
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    thanks
    is there a website tutorial?
    i cant find one on google.
    thanks
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  4. #4
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    If sin(x)=a/b , that gives you all the info you need to construct a right triangle. Remember that sine is a ratio of the opposite leg to the hypotenuse in a right triangle. So a=opposite leg and b=hypotenuse. If you just see a number, meaning not a fraction that means that b=1. You probably already know this, but it's important to these problems.

    You need to know in which quadrants each trig function is positive or negative. In quadrant I all of them are positive but in quadrant II, the leg along the x-axis of the triangle is negative so cos(x) becomes negative. The hypotenuse is always considered positive.

    This Wikipedia page covers a lot of good concepts on this subject. It really requires combining various properties so that you can use the given information to make other conclusions. It's not easy to sum up in a paragraph.

    Trigonometric functions - Wikipedia, the free encyclopedia

    Example: Let's look at sin(x)=0.5. Using whole numbers, the vertical leg is 1 and the hypotenuse is 2. Thus the horizontal leg is the square root of 3. This is found by the Pythagorean Theorem. This is one of the special triangles you need to memorize and has angles of 30deg, 60deg and 90deg. Thus x=30deg.
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  5. #5
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  6. #6
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    Quote Originally Posted by skeeter View Post
    Im sorry but i dont understand what this means. I have read the wikipedia page still dont understand. can you just show me some examples?
    Not being annoying or anything, just want some help with this.

    THanks for your help.
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  7. #7
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    Smile

    Quote Originally Posted by BabyMilo View Post
    Im sorry but i dont understand what this means. I have read the wikipedia page still dont understand. can you just show me some examples?
    Not being annoying or anything, just want some help with this.

    THanks for your help.
    Hello
    Could you tell us what do you don't understand in the image provided.
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  8. #8
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    Quote Originally Posted by Raoh View Post
    Hello
    Could you tell us what do you don't understand in the image provided.
    say sinx=0.5
    then x=30
    but how do i use the diagram to find out all the solutions from -360to360?

    or in another word how to find out -330,-210,150

    thanks
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  9. #9
    Senior Member pacman's Avatar
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    Wolfram|Alpha

    that one one will help a lot
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  10. #10
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    Quote Originally Posted by BabyMilo View Post
    say sinx=0.5
    then x=30
    but how do i use the diagram to find out all the solutions from -360to360?

    or in another word how to find out -330,-210,150

    thanks
    coterminal angles differ by \pm 360 degrees

    30 - 360 = -330

    150 - 360 = -210
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