1. 4.4 Trigonometric
Values of Any Angle
Essential Question:
How do you find the trigonometric values of any
angle?
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2. 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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3. 3

4. Remember that…
All Students Take Calculus
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5. + or -?
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6. Ex. 1﴿ ﴾–2, 3﴿ is a point on the terminal side
of ϴ. Find the six trigonometric functions
for ϴ.
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7. Ex. 2﴿ sin ϴ = 4/5 and tan ϴ < 0. Find cos ϴ.
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8. Ex. 3﴿ tan ϴ = 5/6 and sin ϴ < 0. Find sec ϴ.
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9. The one­handed 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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10. Ex. 4﴿ Evaluate without a calculator.
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11. Going Backwards…
Ex. 5﴿ Find the value﴾s﴿ for ϴ that make the
statement true.
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12. Assignment:
4.4 p. 318 #1, 5, 7, 11, 14, 17­
23 ﴾odd﴿, 29­57 ﴾odd﴿, 61, 62,
81­85 ﴾odd﴿
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