Question

Suppose tan theta= 14/5 and 0 is in the third quadrant . Find sin ( provide 4 decimal places ) .

Answer 1

tan (theta) = 14/5

theta = tan¯¹(14/5) = 70.3° + 180°k where k is an integer.

Since theta is in quadrant III, the angle should be between 180° and 270°.

Let k = 1. Then 70.3° + 180°k = 70.3° + (180° × 1) = 250.3°.

Now the angle is in quadrant III, so we can proceed to evaluate its sine value.

sin(250.3°) = –0.9415