Toán Lớp 11: 1Giúp mình với ạ Tìm GTLN ,GTNN y=3+√cos x 2Giải phương trình sin x=2/5 sin(x+30°) =sin (2x+55) cos(2x+1)=1 cos(x-2)=sin 3(x-n/2

Question

Toán Lớp 11:  1Giúp mình với ạ Tìm GTLN ,GTNN  y=3+√cos x 2Giải phương trình sin x=2/5 sin(x+30°) =sin (2x+55) cos(2x+1)=1 cos(x-2)=sin 3(x-n/2

lantrungbach · Answer

1.  V&igrave; -1&le; cosx &le; 1     n&ecirc;n: 0 &le; &radic;cosx &le; 1        &hArr;0+3 &le; &radic;cosx + 3 &le;1+3        &hArr; 3&le; 3 + &radic;cosx &le; 4         &hArr; 3&le; y&le; 4   ymax = 4 &rArr; cosx = 1 &rArr; x = k2&pi; ( k&isin;Z)   ymin = 3 &rArr; cosx = 0 &rArr; x = &pi;/2 + k&pi; ( k&isin; Z)   2.     a) sinx = 2/5   &hArr; x= arcsin( 2/5) + k2&pi;        x= &pi;-arcsin(2/5) + k2&pi;  ( k&isin;Z)      b) sin(x+ 30 &deg;  ) = sin ( 2x + 55 &deg;)           &hArr; x+ 30&deg;= 2x + 55&deg; + k360&deg;                x+ 30&deg;= 180&deg;-(2x+55&deg;) + k360&deg;           &hArr; x -2x = 55&deg;-30&deg; + k360&deg;                x+ 30 &deg;= 180&deg; -2x - 55&deg; + k360&deg;           &hArr; -x = 25&deg; + k360&deg;                 x + 2x = 180&deg;-55&deg;-30&deg; + k360&deg;           &hArr; x= -25&deg; - k360&deg;               3x= 95&deg; + k360&deg; ( k &isin; Z)        c) cos(2x+1)=1         &hArr; 2x+1 = k2&pi;         &hArr; 2x= -1 + k2&pi;         &hArr; x = -1/2 + k&pi; ( k&isin;Z)         d) cos(x-2)= sin3(x-&pi;/2)         &hArr; cos (x-2) = sin( 3x- 3&pi;/2)         &hArr; cos ( x-2) = cos [ &pi;/2 -( 3x- 3&pi;/2)]         &hArr; cos (x-2) = cos ( -3x + 2&pi;)         &hArr; x-2 = -3x+2&pi; + k2&pi;              x-2 = - ( -3x+2&pi;) + k2&pi;         &hArr; x + 3x = 2 + 2&pi; + k2&pi;              x-2 = 3x - 2&pi; + k2&pi;         &hArr; 4x = 2 + 2&pi; + k2&pi;            x-3x=  2 -2&pi; + k2&pi;         &hArr; x = 1/2 + &pi;/2 + k&pi;/2             -2x= 2-2&pi;+k2&pi;         &hArr; x = 1/2 + &pi;/2 + k&pi;/2              x= -1 + &pi; - k&pi; ( k &isin; Z)