Question

cho \(tan\alpha=\frac{2\sqrt{2}}{3}\) với \(0< \alpha< \frac{\pi}{2}\). tính gtri \(cos\left(\frac{29\pi}{2}-\alpha\right)\)

Answer 1

\(0< a< \frac{\pi}{2}\Rightarrow\left\{{}\begin{matrix}cosa>0\\sina>0\end{matrix}\right.\Rightarrow cosa=\frac{1}{\sqrt{1+tan^2a}}=\frac{3\sqrt{17}}{17}\)

\(\Rightarrow sina=\sqrt{1-cos^2a}=\frac{2\sqrt{34}}{17}\)

\(cos\left(\frac{29\pi}{2}-a\right)=cos\left(14\pi+\frac{\pi}{2}-a\right)=cos\left(\frac{\pi}{2}-a\right)\)

\(=sina=\frac{2\sqrt{34}}{17}\)