Question

已知sina=2/3,cosb=-3/4, a属于(派/2,派).b属于(派,3派/2),求cos(a-b)的值

Answer 1

由题意得：cosa=-√(1-sin²a)=-√5/3，sinb=-√(1-cos²a)=-√7/4
所以，cos(a-b)=cosacosb+sinasinb
=(-√5/3)*(-3/4)+(2/3)*(-√7/4)
=(3√5-2√7)/12

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Answer 2

sina=2/3
cos²a=1-sin²a=1-(2/3)²=5/9
a∈(π/2，π) cosa<0
cosa=-√5/3

cosb=-3/4
sin²b=1-cos²b=1-(-3/4)²=7/16
b∈(π，3π/2) sinb<0
sinb=-√7/4

cos(a-b)=cosacosb+sinasinb
=(-√5/3)(-3/4) +(2/3)(-√7/4)
=(3√5-2√7)/12

Answer 3

sina=2/3 a属于(派/2,派).
∴cosa=-√1-(2/3)²=-√5/3
,cosb=-3/4b属于(派,3派/2),
∴sinb=-√1-(-3/4)²=-√7/4
∴cos(a-b)
=cosacosb-sinasinb
=(-√5/3)(-3/4)-2/3×(-√7/4)
=√5/4+√7/6
=(3√5+2√7)/4

Answer 4

cosa=-√5/3 , sinb=-√7/4
cos(a-b)=cosacosb+sinasinb=(-√5/3)(-3/4)+2/3(-√7/4)=(3√5-2√7)/12