Find csc theta and cot theta if than theta = -4/3 and sin theta > 0

Answer 1

To find csc theta and cot theta, we first need to determine the values of sine and cosine of theta. Since sin theta > 0 and theta is in the second quadrant (where only sin is positive), we know that sin theta = 4/5 (based on the Pythagorean theorem, sin^2 theta + cos^2 theta = 1).

Next, we can find the values of csc theta and cot theta:

csc theta = 1/sin theta = 1/(4/5) = 5/4

cot theta = cos theta/sin theta = sqrt(1 - sin^2 theta) / sin theta = -3/4 / 4/5 = -3/4 * 5/4 = -15/16

Therefore, csc theta = 5/4 and cot theta = -15/16.