Toán Cho Cos a =4\5 , 270 < a < 300 Tính sin ( a + phi\4 ) 12/10/2021 By Aaliyah Cho Cos a =4\5 , 270 < a < 300 Tính sin ( a + phi\4 )
Đáp án: $\dfrac{\sqrt{2}}{10}$ Giải thích các bước giải: $\cos^2a+\sin^2a=1\\\Rightarrow \sin^2a=1-\cos^2a=1-\left (\dfrac{4}{5} \right )^2=\dfrac{9}{25}\\\Rightarrow \sin a=\pm \dfrac{3}{5}$Do $270<a<360\Rightarrow \sin a<0$$\Rightarrow \sin a=-\dfrac{3}{5}\\\sin \left ( a+\dfrac{\pi}{4} \right )\\=\sin a\cos\dfrac{\pi}{4}+\cos a\cos\dfrac{\pi}{4}\\=-\dfrac{3}{5}.\dfrac{\sqrt{2}}{2}+\dfrac{4}{5}.\dfrac{\sqrt{2}}{2}\\=\dfrac{\sqrt{2}}{10}$ Trả lời
Đáp án:
$\dfrac{\sqrt{2}}{10}$
Giải thích các bước giải:
$\cos^2a+\sin^2a=1\\
\Rightarrow \sin^2a=1-\cos^2a=1-\left (\dfrac{4}{5} \right )^2=\dfrac{9}{25}\\
\Rightarrow \sin a=\pm \dfrac{3}{5}$
Do $270<a<360\Rightarrow \sin a<0$
$\Rightarrow \sin a=-\dfrac{3}{5}\\
\sin \left ( a+\dfrac{\pi}{4} \right )\\
=\sin a\cos\dfrac{\pi}{4}+\cos a\cos\dfrac{\pi}{4}\\
=-\dfrac{3}{5}.\dfrac{\sqrt{2}}{2}+\dfrac{4}{5}.\dfrac{\sqrt{2}}{2}\\
=\dfrac{\sqrt{2}}{10}$