- #1
Dethrone
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I did this question using two different trig identities, each of which gave me a different answer when I graphed them on Wolfram Alpha.
1. First identity: sinx = 2sin(0.5x)cos(0.5x)
isolating for sin(0.5x):
sin(0.5x) = (sinx) / (2cos(0.5x))
The question wants sin (0.5 arcsinx):
Applying the formula, we get the answer to be
\(\displaystyle \frac{x}{\sqrt{2(1+\sqrt{1-x^2})}}\)
2. Second identity: sin2x = 0.5 (1-cos2x),
or sin20.5x = 0.5(1-cosx)
Applying that formula, we get the answer to be
\(\displaystyle \sqrt{\frac{1}{2}(1-\sqrt{1-x^2})}\)
Why are the two answers different? Is my algebra wrong somewhere, or is this an issue of domain or something?
1. First identity: sinx = 2sin(0.5x)cos(0.5x)
isolating for sin(0.5x):
sin(0.5x) = (sinx) / (2cos(0.5x))
The question wants sin (0.5 arcsinx):
Applying the formula, we get the answer to be
\(\displaystyle \frac{x}{\sqrt{2(1+\sqrt{1-x^2})}}\)
2. Second identity: sin2x = 0.5 (1-cos2x),
or sin20.5x = 0.5(1-cosx)
Applying that formula, we get the answer to be
\(\displaystyle \sqrt{\frac{1}{2}(1-\sqrt{1-x^2})}\)
Why are the two answers different? Is my algebra wrong somewhere, or is this an issue of domain or something?