-.Cosx+ 1 (x∈R), (1) When the function y reaches the maximum, find the set of independent variables x; (2) What kind of translation and scaling transformation can be obtained from the image of y=sinx(x∈R)? ( 1)y= 2 1cos2x+23sinx？ cosx+ 1 = 4 1(2 cos2x- 1)+4 1+43(2 sinx？ cosx)+ 1 = 4 1 cos2x+4 3 sin2x+45 = 2 1(cos2x？ sin6？ +sin2x？ cos6？ )+45=2 1sin(2x+6？ ) +45 So when y takes the maximum value, it only needs 2x+ 6? =2? +2kπ, (k∈Z), which means x=6? +kπ, (k∈Z). So when the function y takes the maximum value, the set of independent variables x is {x|x=6? +kπ, k∈Z} (2) Transform the function y=sinx as follows: (i) Shift the image of function y=sinx to the left by 6? , get the function y=sin(x+6? ) image; (2) The abscissa of each point on the obtained image is shortened to 2,654,38+0 times (the ordinate is unchanged), and the function y=sin(2x+ 6? ) image; (3) Shorten the ordinate of each point on the obtained image to 2 1 times (the abscissa is unchanged) and get the function y=2 1sin(2x+6? ) image; (iv) moving the obtained image upward by 45 unit lengths to obtain the function y=2 1sin(2x+6? ) +45. To sum up, the image of y = 21cos2x+23 sinx cosx+1is obtained.