Sometimes in problemsolving you only need the sign (plus or minus) of a trigonometric value—not its size.
With three alreadystudied concepts, you have access to the signs of all the trigonometric functions, in all the
quadrants:
$\,\displaystyle\frac{\text{POS}}{\text{NEG}} = \text{NEG}$  $\,\displaystyle\frac{\text{NEG}}{\text{POS}} = \text{NEG}$  $\,\displaystyle\frac{\text{NEG}}{\text{NEG}} = \text{POS}$ 
(positive divided by negative is negative)  (negative divided by positive is negative)  (negative divided by negative is positive) 
By definition, $\,\cos \theta\,$ and $\,\sin\theta\,$ give the $\,x\,$ and $\,y\,$ values
(respectively) of points on the unit circle, as shown at right. It follows that:


By definition, $\displaystyle\,\tan\theta :=\frac{\sin\theta}{\cos\theta}\,$. Therefore:


The (optimistic!) memory device answers the question
in quadrant I, and then proceed counterclockwise. 
This memory device answers the question: Where are the sine, cosine, and tangent POSITIVE? 
The reciprocal of a number retains the sign of the original number. Therefore, in all the quadrants:


On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
