1.求sin^2120°+cos180°+tan45°-cos^2(-330°）+sin(-210°)的值.2.求函数y=-3cos(2X-1/3π)+2的最大值和最小值,并求此时角X的值.

Question

1.求sin^2120°+cos180°+tan45°-cos^2(-330°）+sin (-210°)的值.2.求函数y=-3cos(2X-1/3π)+2的最大值和最小值,并求此时角X的值.

Answer 1

1：原式=sin^2(60°)-1+√2/2-cos^2(360°-330°)+sin(180°-210°)
=(√2-1)/2
2：当2X-1/3π=2Kπ时Y最大,等于5,X=Kπ+1/6π(K∈N)
当2X-1/3π=2Kπ+π时Y最小,等于-1,X=Kπ+2/3π(K∈N)