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4.4 Trigonometric Values of Any Angle
Essential Question:How do you find the trigonometric values of any angle?
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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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Remember that…
All Students Take Calculus
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+ or -?
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Ex. 1﴿ ﴾–2, 3﴿ is a point on the terminal side of ϴ. Find the six trigonometric functions for ϴ.
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Ex. 2﴿ sin ϴ = 4/5 and tan ϴ < 0. Find cos ϴ.
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Ex. 3﴿ tan ϴ = 5/6 and sin ϴ < 0. Find sec ϴ.
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The onehanded 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
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Ex. 4﴿ Evaluate without a calculator.
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Going Backwards…Ex. 5﴿ Find the value﴾s﴿ for ϴ that make the statement true.
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Assignment:
4.4 p. 318 #1, 5, 7, 11, 14, 1723 ﴾odd﴿, 2957 ﴾odd﴿, 61, 62, 8185 ﴾odd﴿