1 points LarPCalc10 54046 v 15 17 cotu v Need Help Read ItWa

1 points LarPCalc10 5.4.046 v) 15 17 cot(u v) Need Help? Read ItWatch t

Solution

We have given sin(u)=-3/5,where 3pi/2<u<2pi, and cos(v)=15/17,where 0<v<pi/2

cos(u)=sqrt(1-sin²(u))=sqrt(1-9/25)=sqrt(16/25)=4/5

cos(u)=4/5

sin(v)=sqrt(1-cos²(v))=sqrt(1-225/289)=sqrt(64/289)=8/17

sin(v)=8/17

cot(u+v)=cos(u+v)/sin(u+v)

=[cos(u)cos(v)-sin(u)sin(v)]/[sin(u)cos(v)+cos(u)sin(v)]

substitute these values sin(u)=-3/5,sin(v)=8/17,cos(u)=4/5,and cos(v)=15/17 into above equation

cot(u+v)=[(4/5)(15/17)-(-3/5)(8/17)]/[(-3/5)(15/17)+(4/5)(8/17)]

=[(60/85)+(24/85)]/[(-45/85)+(32/85)]

=[84/85]/[-13/85]

=(84/85)*(85/(-13))

=-(84/13)

cot(u+v)=-84/13