Finding What Number has the Sine of XDate: 4/12/96 at 19:20:33 From: Anonymous Subject: How to find what number has the sine of x If it is given that the sine of y is x, is there a way to figure out what y is, if x is given? For example, if x is -.9589242747, is it possible to figure out what y is? Date: 7/29/96 at 19:32:34 From: Doctor Jerry Subject: Re: How to find what number has the sine of x Great question! The usual way of solving the equation sin(y) = -0.9589242747 is to use the inverse of the sine function, which is called arcsin. We define arcsin x = y if sin y = x. Because the sine function repeats itself (remember that sin x = sin (x + 2pi) for all x), a convention must be made. It is assumed that -pi <= y <= pi. Then y=arcsin(-0.9589242747) = -1.28318530731. I got this from my calculator, set in radians. But this isn't the only value of y for which sin y = -.9589242747. In fact, all numbers of the form -1.28318530731 + 2pin for some integer n are solutions to your equation. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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