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# 1.56*sin45=1.33sin(theta)

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1.56*sin45=1.33sin(theta)

Guest May 10, 2017
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1.56*sin45=1.33sin(theta)

$$1.56*sin45=1.33sin(\theta)\\ 1.56*\frac{1}{\sqrt2}=1.33sin(\theta)\\ 1.56*\frac{1}{\sqrt2}\div 1.33=sin(\theta)\\ sin(\theta)=0.829388405\\ \theta=sin^{-1}0.829388405\\ \theta \approx 56^\circ 2'9'' \qquad \text{This is just the first quad answer}\\ \text{Sin is positive in the second quad as well}\\ \theta \approx 180^\circ-56^\circ 2'9''\\ \theta \approx 123^\circ 57'51''\\ so\\ \theta \approx 56^\circ 2'9''+2n\pi \quad or \quad \theta \approx 123^\circ 57'51''+2n\pi \quad where\;\; n\in Z\\ \text{Put that together and you get}\\ \theta =180n+(-1)^n*56^\circ 2'9'' \quad where\;\; n\in Z\\$$

Melody  May 10, 2017

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