If sin theta= -7/8, then the value of 1/cot theta in the interval 3pi/2<theta is? okay I've done this question twice. The 1st time I got -7/sqrt15 and the next time got sqrt15/7. Are either of these right or am I totally messed??? I've got myself confused.

Answer 1

sin = opposite / hypotenuse so,
hypotenuse = 8
opposite leg = 7
adjacent leg = sqrt(8^2 - 7^2)
= sqrt(15)
1/cot = tan
tan = opposite / adjacent
= 7/sqrt(15)
in the 4th quadrant the tangent is negative, so add a minus sign:
1/cot(theta) = -7/sqrt(15)