Toán Cho góc a với Sina=3/5. Tính cos2a, cos4a, cos6a và sin3a 17/09/2021 By Autumn Cho góc a với Sina=3/5. Tính cos2a, cos4a, cos6a và sin3a
Đáp án: \(\begin{array}{l} {\mathop{\rm sina}\nolimits} = \dfrac{3}{5}\\ \cos 2a = 1 – 2{\sin ^2}a = \dfrac{7}{{25}}\\ \cos 4a = 2{\cos ^2}2a – 1 = \dfrac{{ – 527}}{{625}}\\ \cos 6a = 4{\cos ^3}2a – 3\cos 2a = \dfrac{{ – 11753}}{{15625}}\\ \sin 3a = 3{\mathop{\rm sina}\nolimits} – 4{\sin ^3}a = \dfrac{{117}}{{125}} \end{array}\) Trả lời
\(\begin{array}{l} \sin a = \frac{3}{5}\\ \Rightarrow \cos 2a = 1 – 2{\sin ^2}a = 1 – 2.{\left( {\frac{3}{5}} \right)^2} = \frac{7}{{25}}.\\ \cos 4a = 2{\cos ^2}2a – 1 = 2.{\left( {\frac{7}{{25}}} \right)^2} – 1 = – \frac{{527}}{{625}}.\\\cos 6a = 4{\cos ^3}2a – 3\cos 2a = \frac{{ – 11753}}{{15625}}\\ \sin 3a = 3\sin a – 4{\sin ^3}a = 3.\frac{3}{5} – 4.{\left( {\frac{3}{5}} \right)^3} = \frac{{117}}{{125}}. \end{array}\) Trả lời
Đáp án:
\(\begin{array}{l} {\mathop{\rm sina}\nolimits} = \dfrac{3}{5}\\ \cos 2a = 1 – 2{\sin ^2}a = \dfrac{7}{{25}}\\ \cos 4a = 2{\cos ^2}2a – 1 = \dfrac{{ – 527}}{{625}}\\ \cos 6a = 4{\cos ^3}2a – 3\cos 2a = \dfrac{{ – 11753}}{{15625}}\\ \sin 3a = 3{\mathop{\rm sina}\nolimits} – 4{\sin ^3}a = \dfrac{{117}}{{125}} \end{array}\)
\(\begin{array}{l} \sin a = \frac{3}{5}\\ \Rightarrow \cos 2a = 1 – 2{\sin ^2}a = 1 – 2.{\left( {\frac{3}{5}} \right)^2} = \frac{7}{{25}}.\\ \cos 4a = 2{\cos ^2}2a – 1 = 2.{\left( {\frac{7}{{25}}} \right)^2} – 1 = – \frac{{527}}{{625}}.\\\cos 6a = 4{\cos ^3}2a – 3\cos 2a = \frac{{ – 11753}}{{15625}}\\ \sin 3a = 3\sin a – 4{\sin ^3}a = 3.\frac{3}{5} – 4.{\left( {\frac{3}{5}} \right)^3} = \frac{{117}}{{125}}. \end{array}\)