Toán Lớp 11: Phương trình lượng giác cơ bản Câu 1. Giải các phương trình sau 1. sin.x = -1/2 2. sinx =√2/2 3. sin3x= √3/2 4. 2sin4x-1=0 5.sin3x=1

Question

Toán Lớp 11:  Phương trình lượng giác cơ bản Câu 1. Giải các phương trình sau  1. sin.x = -1/2 2. sinx =√2/2 3. sin3x= √3/2 4. 2sin4x-1=0 5.sin3x=1

tuenhioanh · Answer

~rai~        (1. sin x=- dfrac{1}{2}   Leftrightarrow  left[ begin{array}{I}x=- dfrac{ pi}{6}+k2 pi  x= pi+ dfrac{ pi}{6}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}x=- dfrac{ pi}{6}+k2 pi  x= dfrac{7 pi}{6}+k2 pi. end{array} right. quad(k in mathbb{Z})   text{Vậy S=} left {- dfrac{ pi}{6}+k2 pi; dfrac{7 pi}{6}+k2 pi Big|k in mathbb{Z} right }.  2. sin x= dfrac{ sqrt{2}}{2}   Leftrightarrow  left[ begin{array}{I}x= dfrac{ pi}{4}+k2 pi  x= pi- dfrac{ pi}{4}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}x= dfrac{ pi}{4}+k2 pi  x= dfrac{3 pi}{4}+k2 pi. end{array} right. quad(k in mathbb{Z})   text{Vậy S=} left { dfrac{ pi}{4}+k2 pi; dfrac{3 pi}{4}+k2 pi Big|k in mathbb{Z} right }.  3. sin3x= dfrac{ sqrt{3}}{2}   Leftrightarrow  left[ begin{array}{I}3x= dfrac{ pi}{3}+k2 pi  3x= pi- dfrac{ pi}{3}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}3x= dfrac{ pi}{3}+k2 pi  3x= dfrac{2 pi}{3}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}x= dfrac{ pi}{9}+k dfrac{2 pi}{3}  x= dfrac{2 pi}{9}+k dfrac{2 pi}{3}. end{array} right. quad(k in mathbb{Z})   text{Vậy S=} left { dfrac{ pi}{9}+k dfrac{2 pi}{3}; dfrac{2 pi}{9}+k dfrac{2 pi}{3} Big|k in mathbb{Z} right }.  4.2 sin4x-1=0   Leftrightarrow  sin4x= dfrac{1}{2}   Leftrightarrow  left[ begin{array}{I}4x= dfrac{ pi}{6}+k2 pi  4x= pi- dfrac{ pi}{6}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}4x= dfrac{ pi}{6}+k2 pi  4x= dfrac{5 pi}{6}+k2 pi end{array} right.   Leftrightarrow  left[ begin{array}{I}x= dfrac{ pi}{24}+k dfrac{ pi}{2}  x= dfrac{5 pi}{24}+k dfrac{ pi}{2}. end{array} right. quad(k in mathbb{Z})   text{Vậy S=} left { dfrac{ pi}{24}+k dfrac{ pi}{2}; dfrac{5 pi}{24}+k dfrac{ pi}{2} Big|k in mathbb{Z} right }.  5. sin3x=1   Leftrightarrow 3x= dfrac{ pi}{2}+k2 pi   Leftrightarrow x= dfrac{ pi}{6}+k dfrac{2 pi}{3}.(k in mathbb{Z})   text{Vậy S=} left { dfrac{ pi}{6}+k dfrac{2 pi}{3} Big|k in mathbb{Z} right }. )