5sin^2(X)+sin(2X)-cos^2(X)=1, 求解X

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/18 00:25:33

5sin^2(X)+sin(2X)-cos^2(X)=1, 求解X
X在0—360度之间

5(sinx)^2+sin2x--(cosx)^2=1
5(sinx)^2+2sinxcosx--(cosx)^2=(sinx)^2+(cosx)^2
4(sinx)^2+2sinxcosx--2(cosx)^2=0
2(sinx)^2+sinxcosx--(cosx)^2=0
(2sinx--cosx)(sinx+cosx)=0
2sinx--cosx=0, sinx+cosx=0
tanx=1/2, tanx=--1
所以　x1=atctan(1/2), x2=360度--arctan(1/2), x3=135度,x4=315度.

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