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January 11th, 2007, 11:24 AM   #11
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We know that sin(x)=3/5
Since sin²(x) + cos²(x) = 1, cos²(x) = 1 - 9/25 = (25-9)/25 = 16/25. Therefore, cos(x) = ±4/5. Since the sin^(-1)(3/5) is in the first quadrant, the cosine must also be positive, and we have cos(x) = 4/5 as an exact answer, and, as a bonus, no calculator was used.
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January 13th, 2007, 03:42 AM   #12
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In an equation such as

w =

is not a power of sin(x); it's a notation for a function called the inverse sine (or invsin or arcsin) of x.

The inverse sine of x is the acute angle whose sine is x, so the equation above implies that x = sin(w). If x is negative, its inverse sine is negative.

Tell me, hatcher777, do you have a textbook which explains the basics of trigonometry (and also mathematical notation in general), including what I've just explained? I ask because your main problem seems to be that you are completely unfamiliar with some of the concepts.

I am willing to explain things here, but it will take time. You could proceed much faster using a good introductory textbook.
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January 13th, 2007, 03:43 AM   #13
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The inverse tangent works rather like inverse sine, but the inverse cosine is a bit different because cosine is an even function, whereas sine and tangent are odd functions.
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