If sin theta 47 and theta is in quadrant IV then find cost

If sin (theta) = - 4/7, and theta is in quadrant IV, then find cos(theta) = tan(theta) = sec(theta) = csc(theta) = cot(theta) =

Given that:

sin () = -4/7 and is in 4th Quadrant

sin() = -4/7

As we know that

Sin²() + Cos²() = 1

Put Sin()= -4/7

Cos²()= 1-(4/7)²

Cos()= (33/49) = (33)/7 ( Cos() would be positive in 4th Qudrant )

Part (a)

Cos() = (33)/7

Part (b)

tan() = sin()/cos() = -4/(33)

Part (c)

sec() = 1/ Cos() = 7/(33)

Part (d)

csc() = 1/sin() = -7/4

Part (e)

Cot() = cos()/sin() = - (33)/4