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Hi Jackie, There are two sine functions in this problem. You know them both because they are both on your calculator. One of them returns the sine of an angle if you input the measure of the angle in degrees and the other returns the sine of an angle if you input the measure of the angle in radians. We usually refer to both of these functions by sin(t) because in a specific problem we know whether we are working in degrees or radians. In this problem you are dealing with both functions so I want to distinguish between them.
What you know from your calculus class is that limit SIN(t)/t approaches 1 as t approaches zero. As Stephen pointed out, if x is the measure of an angle in degrees then y is the measure of the angle in radians if y = x(2π / 360). In this situation sin(x) = SIN(y), it's the same angle you have just used different units to measure it. Thus sin(x)/x = SIN (y)/[y / (2π / 360) ] = (SIN(y)/y) × π/180. Finally as x approaches zero so does y and hence sin(x)/x approaches 1 × π/180 = π/180. I hope this helps,  


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