Some notes on why trig values are positive or negative depending on the quadrant.

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
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2. PC 4.4 Notes 10/12-13/2010
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3. PC 4.4 Notes 10/12-13/2010
Remember that…
All Students Take Calculus
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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.
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5. PC 4.4 Notes 10/12-13/2010
Ex. 2) sin ϴ = 4/5 and tan ϴ < 0. Find cos ϴ.
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6. PC 4.4 Notes 10/12-13/2010
Ex. 3) tan ϴ = 5/6 and sin ϴ < 0. Find sec ϴ.
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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
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8. PC 4.4 Notes 10/12-13/2010
Ex. 5) Evaluate without a calculator.
(BM 10)
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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)
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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)
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11. PC 4.4 Notes 10/12-13/2010
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12. PC 4.4 Notes 10/12-13/2010
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