If cotx=-(3/8), cosx<0, find the cscx.?

Answer 1

sqrt(73)/8

Answer 2

If cotx= -(3/8) and cosx < 0, then we are in the second quadrant.

cotx = cosx/sinx = -3/8

cos²x + sin²x = (-3/a)² + (8/a)² = 1
9 + 64 = a²
a² = 73
a = √73

sinx = 8/a = 8/√73

cscx = 1/sinx = √73 / 8

Answer 3

Cos x <0 puts us in the second or third quadrant.
A negative cot puts us in the second quadrant
By definition of cotangent, the two terms represent two sides of the right triangle, so we find hypotenuse as sqrt(3^2+8^2)= sqrt(73). In second quadrant, sine is positive, so csc x = sqrt(73)/8