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).