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Math Help - Trigonometry Help, Test In 2 days!

  1. #1
    MP3
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    Trigonometry Help, Test In 2 days!

    Hey, i really dont understand this question and i need help

    Each point is on the terminal arm of angle "theta" in standard postion. Find the principal value of "theta to the nearest degree.
    (9, -2)

    I have the answer and it is 348 degrees. I just want to know how you do this question thank you
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  2. #2
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    Quote Originally Posted by MP3 View Post
    Hey, i really dont understand this question and i need help

    Each point is on the terminal arm of angle "theta" in standard postion. Find the principal value of "theta to the nearest degree.
    (9, -2)

    I have the answer and it is 348 degrees. I just want to know how you do this question thank you
    Hello MP3,

    Find the slope of the line which is drawn from the origin through (9, -2). The terminal side of the angle will lie quadrant IV. The slope is -2/9.

    Now use the inverse tangent (arctan) of -2/9 to find the angle the line makes with the x-axis. In this case, it's about -12.5 degrees if we rotate theta in a clockwise direction. From the initial side to the terminal side rotating in a counterclockwise direction we arrive at -12.5 + 360 = 347.5 or approximately 348 degrees.
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    MP3
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    Hey thank you but i have one last question to ask you, i just want to understand why would you add 360 in this question?

    Quote Originally Posted by masters View Post
    Hello MP3,

    Find the slope of the line which is drawn from the origin through (9, -2). The terminal side of the angle will lie quadrant IV. The slope is -2/9.

    Now use the inverse tangent (arctan) of -2/9 to find the angle the line makes with the x-axis. In this case, it's about -12.5 degrees if we rotate theta in a clockwise direction. From the initial side to the terminal side rotating in a counterclockwise direction we arrive at -12.5 + 360 = 347.5 or approximately 348 degrees.
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    Quote Originally Posted by MP3 View Post
    Hey thank you but i have one last question to ask you, i just want to understand why would you add 360 in this question?
    Hello MP3,

    You could say subtract 12.5 degrees from 360 degrees. We need the positive angle theta formed with the x-axis by the line through the origin and (9, -2).

    Either way you're going to get the angle formed by rotating the initial side from the positive side of the x-axis all the way around until it coincides with the terminal side of -12.5 degrees. See diagram.

    -12.5 degrees and 347.5 degrees have the same terminal side.
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    MP3
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    Wow thank you very much, you saved my day for tomorrow, thanks again!

    Quote Originally Posted by masters View Post
    Hello MP3,

    You could say subtract 12.5 degrees from 360 degrees. We need the positive angle theta formed with the x-axis by the line through the origin and (9, -2).

    Either way you're going to get the angle formed by rotating the initial side from the positive side of the x-axis all the way around until it coincides with the terminal side of -12.5 degrees. See diagram.

    -12.5 degrees and 347.5 degrees have the same terminal side.
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  6. #6
    MP3
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    Hey Masters, a few more questions

    Okay same question as stated above but with these new cordinates

    1) (-4, -7)

    2) (-5, 9)

    3) (5, 11)
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    Quote Originally Posted by MP3 View Post
    Okay same question as stated above but with these new cordinates

    1) (-4, -7)

    2) (-5, 9)

    3) (5, 11)
    Hi MP3,

    You just need to sketch a graph to show where the point is. Draw a line from the origin through that point. Find the slope between (0, 0) and the point and then the inverse tangent (arctan) of that slope.

    The arctan on your calculator is probably \tan^{-1}.

    I'll do the first one for you, but you should practice on the other two.

    1) First find the slope between (0, 0) and (-4, -7)

    m=\frac{Y_2-y_1}{x_2-x_1}=\frac{-7-0}{-4-0}=\frac{7}{4}

    Next, find \tan^{-1}\frac{7}{4}\approx 60.3^{\circ}

    Notice that the terminal side is in quadrant III. The angle you just found was the angle that line made with the x-axis. See diagram. To find angle theta which is the complete rotation from the initial side of the x-axis to that terminal side, we need to add 180 degrees. Do you see that?
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