This document provides instruction on finding trigonometric values for any angle. It includes examples of finding sine, cosine, and tangent values for specific angles in different quadrants. It also discusses using reference angles to determine the correct sign when the angle is in a particular quadrant. Students are given examples of evaluating trigonometric functions without a calculator and finding possible angle values that make trigonometric statements true. The document concludes with assignment problems for students to practice these skills.

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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