trigonometric questions on quadrants urgent

[nez1993]

Find the trigonometric functions for tan theta= -4/3 and sin theta<0?
I know that this means that the value is in Quadrant 4 because in Quadrant 4 tan is negative and sin is negative. Then tan is b/a which means we need to find radius and radius is 5, so how do I know if the radius if positive 5 or negative 5? so how do you know if its negative , just because its in quadrant 4 what does it become then?

 

[Deleted member 4993]

Find the trigonometric functions for tan theta= -4/3 and sin theta<0?
I know that this means that the value is in Quadrant 4 because in Quadrant 4 tan is negative and sin is negative. Then tan is b/a which means we need to find radius and radius is 5, so how do I know if the radius if positive 5 or negative 5? so how do you know if its negative , just because its in quadrant 4 what does it become then?

The radius (or the hypotenuse) is considered positive - always.

In the fourth quadrant - the ADJACENT part (base) is positive and the OPPOSITE (height) is negative.