字典翻译 问答 小学 数学 三角函数的题.麻烦了.Findalltheanglesbetween0°and360°:(1)sin(2x-30°)=cos30°(2)3sinYcosY=2cos^2Y(3)2tan^2Z+11secZ+7=0详细过程.麻烦了
问题标题:
三角函数的题.麻烦了.Findalltheanglesbetween0°and360°:(1)sin(2x-30°)=cos30°(2)3sinYcosY=2cos^2Y(3)2tan^2Z+11secZ+7=0详细过程.麻烦了
问题描述:

三角函数的题.麻烦了.

Findalltheanglesbetween0°and360°:

(1)sin(2x-30°)=cos30°

(2)3sinYcosY=2cos^2Y

(3)2tan^2Z+11secZ+7=0

详细过程.麻烦了

潘志庚回答:
  sin(2x-30°)=sqrt(3)/2   x∈[0,2π]=>(2x-30°)∈[-π/6,4π-π/6]   =>2x-30°=mπ/3+nπ,(m=1,2;n=1,2,3)   =>x=...   (2)   2cos^2Y-3sinYcosY=0   cos^2Y(2-3tanY)=0   =>cosY=0ortanY=2/3Y∈[0,2π]   =>Y=π/2,arctan(2/3),arctan(2/3)+π   (3)   2(sec^2Z-1)+11secZ+7=0   2sec^2Z+11secZ+5=0   (2secZ+1)(secZ+5)=0   secZ=-1/2orsecZ=-5   cosZ=-2(del),-1/5Z∈[0,2π]   =>Z=arccos(-1/5),2π-arccos(-1/5)
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