Solving a Trig EquationDate: 3/11/96 at 10:24:36 From: Mueen Nawaz Subject: Trig stuff Hi. I have a question. Suppose I know the value for the expression: (sin (alpha))/(alpha) That's sine alpha divided by alpha. How will I find alpha? Let's assume the value is 1/60. What's alpha? Mueen Nawaz Date: 7/3/96 at 22:38:57 From: Doctor Jerry Subject: Re: Trig stuff To solve sin(x)/x=1/60 for x (or alpha) is not possible if you want to do it "exactly." The equation 2x+3 = 1/60 can be solved exactly or analytically or in closed form, but sin(x)/x = 1/60 can't be solved in this way. You may solve it graphically by plotting the function f(x)=sin(x)/x-1/60 and noticing the value of x where it crosses the x-axis. Or you can use the bisection method or Newton's method or any one of the root finders on a calculator. I found x to be approximately 3.09006 on my calculator. -Doctor Jerry, The Math Forum |
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