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 January 11th, 2007, 11:24 AM #11 Senior Member   Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 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.
 January 13th, 2007, 03:42 AM #12 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2205 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.
 January 13th, 2007, 03:43 AM #13 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2205 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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# exact value of cos(4pi/5)

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