三角函數相關應用問題(求詳解)

Question

1.sin^(30+A)+sin^(60-A)+cos^(45+A)+cos^(45-A)=?

2.90Σk=1(sink)+90Σk=1【cos(90+k)】=?

Answer 1

1.
sin(30+A)
= -sin(-30-A)
= cos(90-30-A)
= cos(60-A)
cos(45-A)
= cos(A-45)
= sin(90 + A - 45)
= sin(45+A)
sin2(30+A)+sin2(60-A)+cos2(45+A)+cos2(45-A)
= cos2(60-A)+sin2(60-A) + cos2(45+A)+sin2(45+A)
= 1 + 1
= 2
2. cos(90+k) = -sink
Σk=190[sin(k)] + Σk=190 [cos(90+k)]
= Σk=190[sin(k)] + Σk=190 [-sin(k)]
= Σk=190[sin(k)] - Σk=190 [sin(k)]
= 0
如果有問題, 請來函討論. 不然, 我可能會錯失你再補充的疑點.