题目

已知sin3A+2sin^3 A=1(90度

提问时间：2021-04-15

答案

1.sin3a=3sina-4(sina)^3
sin3A+2sin^3 A=1
3sinA-2(sinA)^3=1
2(sinA)^3-3sinA+1=0
(2sinA-1)(sinA-1)=0
sinA=1/2,sinA=1
90度sinA=1/2
cos2A=1-2(sinA)^2=1/2
2.
3sin2A-2sin2B=0
3-6sin^A-(2-4sin^B)=0
1-6sin^A+4sin^B=0
6sin^A-4sin^B=1 (1)
3sin^A+2sin^B=1 (2)
(1)+(2)*2
12sin^A=3
sin^A=1/4,sinA=1/2,cosA=根号3/2,A=30
sin^B=1/8,sinB=根号2/4,cosB=根号14/4,
sin2B=根号7/4,cos2B=3/4
3.
设PA与AB夹角为X度
PR=100-90*sinX
CR=100-90*cosX
S=PR*CR
=(100-90*sinX)*(100-90*cosX)