State the quadrant in which theta lies when theta satisfies

State the quadrant in which theta lies when theta satisfies csc theta

Solution

1)csc<0, cot<

=>1/sin<0 ,sin/cos <0

=>sin<0 ,cos>0

in 4th quadrant

2)arclength s =(pi/180^o)r

arclength s =(pi/180^o)115^o*6

arclength s =12

area = (pi/180^o)(/2)r²

area = (pi/180^o)(115^o/2)6²

area = 36.13 square units