The document contains notes from a trigonometry class discussing trigonometric functions of any angle. It provides examples of calculating sine, cosine, and tangent values for various angles in different quadrants. It also includes example problems solving for trigonometric functions given other information about an angle. The document concludes with an assignment problem set.

1. PC 4.4 Notes 10/12-13/2010
4.4: Trigonometric Functions of
Any Angle
Find the sine, cosine, and tangent of the following
angles and determine what quadrant they terminate in.
Angle Quadrant sin cos tan
130° II 0.766 –0.643 –1.192
290° IV –0.940 0.342 –2.747
5π/4 III –0.707 –0.707 1
2π/9 I 0.643 0.766 0.839
Fjelstrom

2. PC 4.4 Notes 10/12-13/2010
Fjelstrom

3. PC 4.4 Notes 10/12-13/2010
Remember that…
All Students Take Calculus
Fjelstrom

4. PC 4.4 Notes 10/12-13/2010
Ex. 1) (–2, 3) is a point on the terminal side
of ϴ. Find the six trigonometric functions
for ϴ.
Fjelstrom

5. PC 4.4 Notes 10/12-13/2010
Ex. 2) sin ϴ = 4/5 and tan ϴ < 0. Find cos ϴ.
Fjelstrom

6. PC 4.4 Notes 10/12-13/2010
Ex. 3) tan ϴ = 5/6 and sin ϴ < 0. Find sec ϴ.
Fjelstrom

7. PC 4.4 Notes 10/12-13/2010
The one-handed trick…
When evaluating trig
functions:
Step 1) Find the trig
function for the
reference angle
Step 2) Determine the
sign (+ or -) for the
value based on the
terminating quadrant.
More info at http://function-of-time.blogspot.com/2009/08/trig-reference-angle-
cheat-hand.html
Fjelstrom

8. PC 4.4 Notes 10/12-13/2010
Ex. 5) Evaluate without a calculator.
(BM 10)
Fjelstrom

9. PC 4.4 Notes 10/12-13/2010
Going Backwards…
Ex. 6) Find the value(s) for ϴ that make the
statement true. (BM 11)
Fjelstrom

10. PC 4.4 Notes 10/12-13/2010
Assignment:
#16 p. 318 #1, 5, 7, 11, 14,
17-23 (odd), 29-57 (odd), 61,
62, 81-85 (odd)
Fjelstrom

11. PC 4.4 Notes 10/12-13/2010
Fjelstrom

12. PC 4.4 Notes 10/12-13/2010
Fjelstrom