5.1. The Unit Circle http://www.ck12.org
Guided Practice
- Using knowledge of the first quadrant of the unit circle, identify the angles and important points of the third
quadrant. - For each of the six trigonometric functions, identify the quadrants where they are positive and the quadrants where
they are negative. - Evaluate the following trigonometric expressions using the unit circle.
a. sinπ 2
b. cos 210◦
c. tan 315◦
d. cot 270◦
e. sec^116 π
f. csc−^54 π
Answers: - Both thexvalues andyvalues are negative and their respective coordinates correspond to those of the other
quadrants. - In quadrant I, the hypotenuse, adjacent and opposite side are all positive. Thus all 6 trigonometric functions are
positive.
In quadrant II the hypotenuse and opposite sides are positive and the adjacent side is negative. This means that
every trigonometric expression involving an adjacent side is negative. Sine and its reciprocal cosecant are the only
two trigonometric functions that do not refer to the adjacent side which makes them the only positive ones.
In quadrant III only the hypotenuse is positive. Thus the only trigonometric functions that are positive are tangent
and its reciprocal cotangent because these functions refer to both adjacent and opposite sides which will both be