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Section 5 Mathematical Formulas
5-1 Trigonometric Function
5-1-9 Composition Formula of Trigonometric Function
【Composition in "sin" 】
\begin{eqnarray}
a sin\theta+b cos\theta=\sqrt{a^2+b^2}sin(\theta+\alpha) \nonumber
\end{eqnarray}
Note the fololowing.
\begin{eqnarray}
sin\alpha=\frac{b}{\sqrt{a^2+b^2}}\;\;\;\;\;cos\alpha=\frac{a}{\sqrt{a^2+b^2}}\;\;\;\;\;tan\alpha=\frac{b}{a} \nonumber
\end{eqnarray}
【Composition in "cos"】
\begin{eqnarray}
a sin\theta+b cos\theta=\sqrt{a^2+b^2}cos(\theta-\beta) \nonumber
\end{eqnarray}
Note the fololowing.
\begin{eqnarray}
sin\beta=\frac{a}{\sqrt{a^2+b^2}}\;\;\;\;\;cos\beta=\frac{b}{\sqrt{a^2+b^2}}\;\;\;\;\;tan\beta=\frac{a}{b} \nonumber
\end{eqnarray}
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