1)It is given that sinA+cosB=2/5.Find the value of the following expressions
a)sin2A
b)cos4A
c)sin^4 A+cos^4 A
For each of the fowllowing identities in A,find r and B,where r>0 and 0 < B < 90.Correct B to 2 decimal places.
2)3sinA-4cosA=r sin(A-B)
3)8cosA-15sinA=r cos(A+B)
A.Math Double Angle Formulae The Subsidiary Angle Form
2008-05-12 8:03 am
回答 (1)
2008-05-12 5:00 pm
✔ 最佳答案
(a)sinA+cosB=2/5(sinA+cosA)2=(2/5)^2
1+2sinAcosA=4/25
2sinAcosA=-21/25
sin2A=-21/25
(b)cos4A=1-2sin22A
=1-2(-21/25)2
=-257/625
(c)sin4A+cos4A=(sin2A+cos2A)2 -2sin2Acos2A
=1-2sin2Acos2A
=1-1/2sin22A
=1-1/2(-21/25)2
=809/1250
(b)3sinA-4cosA=5[sinA(3/5)-cosA(4/5)]
=5sin(A-52.13˚)
8cosA-15sinA=17[cosA(8/17)-sinA(15/17)]
=17cos(A+61.93˚)
收錄日期: 2021-04-23 20:35:41
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