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Math Help - Simple Trigonometric Equations

  1. #1
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    Simple Trigonometric Equations

    These are hard for me right now, it will be fine once I understand it but I'm not sure because it's very confusing!

    If I had cos 3x = 0.5, would I:
    Use cos^-1 0.5 = 60
    and because cos is positive in the second quadrant, would I add the 60 to 90 to make 150...
    then divide both answers by 3 to get 20 and 50?

    Is this right, and would it work for any other including sin?

    Also if I had tan x = -root 3, would I solve it like:
    tan^-1 root 3 = 60
    and because tan is positive in the third quadrant, would I add the 60 again to 180 to make 240
    and are my solutions 60 and 240, and nothing else?
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  2. #2
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    Trigonometry

    Hello db5vry
    Quote Originally Posted by db5vry View Post
    If I had cos 3x = 0.5, would I:
    Use cos^-1 0.5 = 60
    and because cos is positive in the second quadrant, would I add the 60 to 90 to make 150...
    then divide both answers by 3 to get 20 and 50?
    Look at the attached diagram, showing \cos 60^o = 0.5. The other angle in the diagram whose cosine is also 0.5 is in the fourth quadrant: it is 360^o - 60^o = 300^o.

    If we allow angles of more than 360^o, the next angle whose cosine is 0.5 is 360 + 60 = 420^o; the next is 660^o, and so on.

    So if \cos 3x = 0.5, the possible values of 3x are 60^o, 300^o, 420^o, 660^o, \dots

    To find the values of x, then, you'll need to divide each of these by 3 to get:

    x = 20^o, 100^o, 140^o, 220^o, \dots

    (Cosine is positive in the first and fourth quadrants, of course.)

    Grandad
    Attached Thumbnails Attached Thumbnails Simple Trigonometric Equations-untitled.jpg  
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  3. #3
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    Quote Originally Posted by Grandad View Post
    Hello db5vryLook at the attached diagram, showing \cos 60^o = 0.5. The other angle in the diagram whose cosine is also 0.5 is in the fourth quadrant: it is 360^o - 60^o = 300^o.

    If we allow angles of more than 360^o, the next angle whose cosine is 0.5 is 360 + 60 = 420^o; the next is 660^o, and so on.

    So if \cos 3x = 0.5, the possible values of 3x are 60^o, 300^o, 420^o, 660^o, \dots

    To find the values of x, then, you'll need to divide each of these by 3 to get:

    x = 20^o, 100^o, 140^o, 220^o, \dots

    (Cosine is positive in the first and fourth quadrants, of course.)

    Grandad
    Thank you for this help!

    Of course I remember cosine is positive in the fourth now! It's sine that is positive in the second, don't know why I thought that..
    But that was excellent thanks very much!
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