Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) < 0, csc (t) > 0.

Question

Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) < 0, csc (t) > 0.

Answer 1

Check the problem again!

Cosecant (csc) is the reciprocal of sine (sin) so they are always either both positive or both negative.

 

Perhaps it should be sine < 0 and cosine > 0?

 

In that case, sine is less than zero in quadrants 3 and 4, and cosine is greater than zero in quadrants 1 and 4, so this angle can only lie in quadrant 4.

 

On the unit circle, remember that cosine is the x-coordinate of the terminal side of the angle and sine is the y-coordinate.  Quadrant 1 is that where both sine and cosine are greater than zero.  The rest of them are numbered consecutively going counter-clockwise; so quadrant 2 has cos < 0 and sin > 0, quadrant 3 has cos < 0 and sin < 0, and quadrant 4 has cos > 0 and sin < 0