cot a if sin a35 and cos a

cot a, if sin a=-3/5 and cos a <0

no calculator

Solution

To find cot a

Given sin a = -3/5

sine is negative so it must in 3rd or 4th quadrant,

as it is also given that cos a is negative, we shall fix the quadrant as 3rd

(in 4th quadrant cos is positive)

Now from the identity

sin²a+cos²a=1

cos²a = 1-sin²a

=1- (-3/5)²

= 1-(9/25)

= 16/25

so

cos²a = 16/25

i.e., cos a = +4/5 and cos a = -4/5

we choose cos a = - 4/5 from the initial discussion

Finally we have

cos a = - 4/5

sin a = -3/5

and cot a = cos a /sin a

= (-4/5)/(-3/5)

= (4/3)