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Math Help - Defining only in terms of a unit circle

  1. #1
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    Defining only in terms of a unit circle

    We ofcourse know that given a unit circle, certain values of trigonometric functions apply ( \displaystyle sin\frac {\pi}{4}=\frac {\sqrt2}{2}, for example).

    However, if we were to take a circle with a bigger radius, that would automatically lead the values of such functions to change.

    Whenever i used sin(pi/4) in a problem i always took its value as the one mentioned in terms of a unit circle, when in fact it varies according to the lengths of the triangle.

    So my question would be: How can we take \displaystyle sin\frac {\pi}{4} as having a standard value of \frac {\sqrt2}{2} when in fact it varies. What am i missing here?
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    Because when you scale the radius by a factor of \displaystyle r, the perpendicular (sine value) is also scaled by a factor of \displaystyle r.

    So to find the sine value, you have to divide by the radius.
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  3. #3
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    Sorry for my mistake, i was used to the unit circle where the radius was 1, thus the sine was actually the perpendicular itself. When i went to a bigger circle i forgot to divide it by the hypothenuse of the drawn triangle and i was still taking the value of the sine as being equal to the perpendicular itself. Also since sine is a ratio between the sides of a triangle it would have been illogical to exceed one. I'm sorry for my stupid question.

    Thank you for the reply.
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