If sin theta is -4/5. 270 degrees is less than theta and theta is less than 360 degrees. what is tan theta?

tan theta = -4/3.

Step-by-step explanation:

The inequality means that theta is in the 4th quadrant ( between 270 and 360 degrees.

The angle whose sine is 4/5  is 53.13 degrees.

So the angle whose sine is -4/5 is 306.87 degrees.

The tangent is negative and  the triangle formed by the angle in the 4th quadrant has sides   3, - 4 and 5  ( by the Pythagoras theorem).

So tan theta =  opposite / adjacent = -4/3  (answer).