Question

直角坐标系xoy中,角a的始边为x轴非负半轴,终边为射线l:y=（2根号2）x,(x>=0) （1）求sin(a+30°

Answer 1

1

射线l:y=2√2x (x>=0)

tana=2√2 cosa>0,sina>0

(cosa)^2=1/(1+(tana)^2)=1/9

cosa=1/3 sina=2√2/3

sin(a+30)=sinacos30+cosa*sin30=(2√2/3)(√3/2)+(1/3)*(1/2)=(1+2√6)/6

2

p(x0,0),q(x1,2√2x1)

pq^2=(x0-x1)^2+(2√2x1)^2=x0^2+9x1^2-2x0x1=16

Spoq=x0 *(2√2x1)/2=x0*(√2x1)