Sin, csc, cos, sec, tan, cot

If sin is negative, is csc negative? the same for the other trig functions as well

For csc, yes. However, if the sin is negative the cos may or may not be negative.

A. csc = 1/sin
B. cos = cos
C. sec = 1/cos
D. tan = sin/cos
E. cot = cos/sin

If the sin is negative and the cos is positive, then A, D, and E are negative.

However, if if the sin is negative and the cos is negative,
then A, B, C and negative.

If the sin is positive and the cos is negative,
then B, C, D, and E are negative

Since the sin and cos may both be negative and/or positive at different times in their cycle, the answer also depends on what angle you are talking about.

The sin and cos are both positive in quadrant 1, the sin is positive but the cos is negative in quadrant 2, both are negative in quadrant 3, and the sin is negative but the cos is positive in quadrant 4.

Jim

sin = 1/csc
cos = 1/sec
tan = 1/cot
so if the equation of one is negative then you have to make the second part negative as well.

Yes. It's just the reciprocal, remember!