ArcSin Approximations
Example 3: Determine the derivative of . Here we recognize that arcsin(u) = sin-1(u). We also use the trig identity sin2(x) + cos2(x) = 1. Depending on the value of x, this last expression will simplify to either 1 or –1. On the interval -π < x < π, the ratio is –1 when x < 0 and is 1 when x > 0. Example 4: Evaluate . ... ................
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