PC 4.4 Notes Fjelstrom 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
Some notes on why trig values are positive or negative depending on the quadrant.
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PC 4.4 Notes
Fjelstrom
10/12-13/2010
4.4: Trigonometric Functions of Any AngleFind 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
PC 4.4 Notes
Fjelstrom
10/12-13/2010
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Remember that…
All Students Take Calculus
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Ex. 1) (–2, 3) is a point on the terminal side of ϴ. Find the six trigonometric functions for ϴ.
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Ex. 2) sin ϴ = 4/5 and tan ϴ < 0. Find cos ϴ.
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Ex. 3) tan ϴ = 5/6 and sin ϴ < 0. Find sec ϴ.
PC 4.4 Notes
Fjelstrom
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The one-handed trick…When evaluating trig functions:Step 1) Find the trig function for the reference angleStep 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
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Ex. 5) Evaluate without a calculator. (BM 10)
PC 4.4 Notes
Fjelstrom
10/12-13/2010
Going Backwards…
Ex. 6) Find the value(s) for ϴ that make the statement true. (BM 11)