http://www.ck12.org Chapter 5. Trigonometric Functions
negative.
In quadrant IV the hypotenuse and the adjacent sides are positive while the opposite side is negative. This means
that only cosine and its reciprocal secant are positive.
A mnemonic device to remember which trigonometric functions are positive and which trigonometric functions are
negative is “AllStudentsTakeCalculus.” All refers to all the trigonometric functions are positive in quadrant I. The
letter S refers to sine and its reciprocal cosecant that are positive in quadrant II. The letter T refers to tangent and its
reciprocal cotangent that are positive in quadrant III. The letter C refers to cosine and its reciprocal secant that are
positive in quadrant IV.
- a. sinπ 2 = 1
b. cos 210◦=−
√ 3
2
c. tan 315◦=− 1
d. cot 270◦= 0
e. sec^116 π=cos^1116 π= √^23 =^2
√ 3
3f. csc−^54 π=sin^1 − 54 π=−√^22 =−
√
2
Practice
Name the angle between 0◦and 360◦that is coterminal with...
1.− 20 ◦
- 475◦
3.− 220 ◦ - 690◦
5.− 45 ◦
Use your knowledge of the unit circle to help determine whether each of the following trigonometric expressions is
positive or negative. - tan 143◦
- cosπ 3
- sin 362◦
- csc^34 π
Use your knowledge of the unit circle to evaluate each of the following trigonometric expressions. - cos 120◦
- secπ 3
- tan 225◦
- cot 120◦
- sin^116 π
- csc 240◦
- Find sinθand tanθif cosθ=
√ 3
2 and cotθ>0.- Find cosθand tanθif sinθ=−^12 and secθ<0.