解:1.cos(270°+α )=cos(90°+180°+ α )=-sin(180°+α )= -1/32.cos(α -9π )= - cosα=-3/5,所以cosα=3/5, 因为π< α<2 π所以3π/2<α<2π,即α在第四象限,所以sinα=-4/5cot(α -11π/2 )=-tanα=4/33.sinα+cosα=（√3 +1）/2,两边平方:1+2sinα*cosα=1+√3/2所以sinα*cosα=√3/4又sinα*cosα=m/2,所以m=√3/24.sinα=12/13,α∈(0,π/2),所以cosα=5/13cos(π-α)=-cosα=-5/135.g(x)=sin4x的周期为π/2f(x)=1-2(sinwx)^2=cos2wx周期为π,所以2π/2w=π,所以w=16. sin(-2109°)+cos1941°=sin(51°-6*360°)+cos(90°+51°+5*360°)=sin51°-sin51°=07.cot(-35π/3)=cot(-12π+π/3)=cot(π/3)=√3/3