Expert: Sherry Wallin - 12/1/2010

Question
I'm confused as to how to find out what quadrant it is in if the problem given is secA= 6/5 , tanA < 0

Answer
Hi Rachel~

The sec A is 1/cos A, correct? Where is the cos A negative? Wherever x is negative, in QII and QIII. Where is the cos A positive? Yes, wherever x is positive, which is in QI and QIV, so the same will be true for the secant function. Now, you are given that tan A is negative, i.e., you were given tan A < 0, and you know that the tangent function is just a ratio of the sin A/cos A, then you will want to know when the sin A and the cos A have opposite signs because that is when the tangent function will be negative. That occurs when x has a different sign as y. That can only occur in QII and QIV where in QII, x is negative and y positive, and in QIV, x is positive and y is negative. Now all you have to do is look at the intersection of QI and QIV (because we are looking for when sec A = 1/cos A which is like 1/x is positive) with QII and QIV, and that just so happens to be QIV.

Math Prof