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Math Help - the waves of sin and cosine and tangent

  1. #1
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    the waves of sin and cosine and tangent

    i have been trying to understand the graphs and what they mean
    i see that some area on the wave have 90 degrees angle despite it not being the little box that indicates right triangles and then suddenly it turns to 270 while in similar graphs that same place would be 180 despite the wave size being the same
    anyone have the ability to simplify this?
    tangent seems even more complicated what does the twisted line have to do with it being a division of sine and cosine
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  2. #2
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    Re: the waves of sin and cosine and tangent

    Quote Originally Posted by ariel32 View Post
    i have been trying to understand the graphs and what they mean
    i see that some area on the wave have 90 degrees angle despite it not being the little box that indicates right triangles and then suddenly it turns to 270 while in similar graphs that same place would be 180 despite the wave size being the same
    anyone have the ability to simplify this?
    It is difficult to understand your question. What does it mean for an area to have a certain angle? What does it mean for an area to be a little box? What does it mean for an area to turn 270?
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  3. #3
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    Re: the waves of sin and cosine and tangent

    i am just saying that in sine the same looking shapes have different angle values compared to consine
    also i know that tangent is a line going from right to left in a twist and dont understand why
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  4. #4
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    Re: the waves of sin and cosine and tangent

    Quote Originally Posted by ariel32 View Post
    i am just saying that in sine the same looking shapes have different angle values compared to consine
    Does it surprise you that sine has a different graph from cosine? They are different functions, after all... There are identities \cos(\pi/2-x)=\sin(x) and \cos(-x)=\cos(x). Thus, \sin(x)=\cos(\pi/2-x)=\cos(-(x-\pi/2))=\cos(x-\pi/2). The graph of \cos(x-\pi/2) is the graph of \cos(x) moved \pi/2 to the right. Therefore, the graph of sin(x) is obtained from that of cos(x) by moving the latter \pi/2 to the right, and the graph of cos(x) is that of sin(x) moved \pi/2 to the left.
    Quote Originally Posted by ariel32 View Post
    also i know that tangent is a line going from right to left in a twist and dont understand why
    This is what you get when you calculate the coordinates of the point on the graph according to the formula for tangent. In particular, tan(0) = 0 because sin(0) = 0, but when x approaches \pi/2 from the left, cos(x) approaches 0 and sin(x) approaches 1, so sin(x) / cos(x) grows indefinitely.

    Have you read any textbook or other source, such as Wikipedia, about trigonometric functions? Perhaps you can ask specific questions that you get in the process.
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