Tan a=2 tính Cos^2a
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(0< a< \dfrac{\Omega}{2}\)
=>\(sina>0\)
=>\(sina=\sqrt{1-cos^2a}=\dfrac{4}{5}\)
\(\dfrac{3}{2}\Omega< b< 2\Omega\)
=>\(sinb< 0\)
=>\(sinb=-\sqrt{1-\left(\dfrac{12}{13}\right)^2}=-\dfrac{5}{13}\)
\(tana=\dfrac{sina}{cosa}=\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{4}{3}\)
\(tanb=\dfrac{sinb}{cosb}=\dfrac{-5}{13}:\dfrac{12}{13}=-\dfrac{5}{12}\)
\(tan\left(a+b\right)=\dfrac{tana+tanb}{1-tana\cdot tanb}\)
\(=\dfrac{\dfrac{4}{3}+\dfrac{-5}{12}}{1-\dfrac{4}{3}\cdot\dfrac{-5}{12}}=\dfrac{11}{12}:\left(1+\dfrac{20}{36}\right)=\dfrac{11}{12}:\dfrac{14}{9}\)
\(=\dfrac{11}{12}\cdot\dfrac{9}{14}=\dfrac{11\cdot3}{4\cdot14}=\dfrac{33}{56}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
d) \(A=3cm\); \(\omega=4\pi\left(rad/s\right)\); \(\varphi_0=\dfrac{\pi}{5}\left(rad\right)\)
Khi đó \(T=\dfrac{2\pi}{\omega}=0,5\left(s\right)\)
Cho \(x=1,5cm\Leftrightarrow\varphi=\pm\dfrac{\pi}{3}\left(rad\right)\)
Thời gian vật đi qua vị trí \(x=1,5cm\) lần thứ ba là:
\(T+t_d=0,5+\dfrac{\Delta\varphi_d}{2\pi}.T\)
\(=0,5+\dfrac{\dfrac{\pi}{3}-\dfrac{\pi}{5}}{2\pi}.0,5\)
\(=\dfrac{8}{15}\left(s\right)\)
e) Thời gian cần tìm là:
\(t_e+19T=\dfrac{\Delta\varphi_e}{2\pi}.T+19.0,5\)
\(=\dfrac{\dfrac{4\pi}{3}}{2\pi}.0,5+9.5=\dfrac{59}{6}\left(s\right)\)
\(1+tan^2\alpha=\dfrac{1}{cos^2\alpha}\Rightarrow1+2^2=\dfrac{1}{cos^2\alpha}\\ \Rightarrow5=\dfrac{1}{cos^2\alpha}\Rightarrow cos^2\alpha=\dfrac{1}{5}\)