4.4 Trigonometric Functions of Any Angle
Note:
r is always
positive!
Example: The point (3, ­4) is on the terminal side of angle θ. Find the exact value of each of the six trigonometric functions of θ.
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Example: The point (­1, ­3) is on the terminal side of angle θ. Find the exact value of each of the six trigonometric functions of θ.
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Recall where each trig function is positive and negative, and use that information to determine the quadrant in which θ lies, given the following information:
1) cos θ > 0, tan θ > 0
2) sin θ < 0, tan θ < 0
Find the exact value of each of the remaining trigonometric functions of θ, given the following:
1)
2)
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Give the exact value of each of the following, if possible.
1) tan (­π)
2) csc π
3) sec π/4
4) cot π/4
5) sec π/3
6) csc π/3
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A reference angle is a positive acute angle in standard position which has the same cosine and sine as a given angle, except perhaps for the SIGN (+/­).
Determine the reference angle of each of the following angles.
1) 31π/6
2) ­π/4
3) 5π/3
4) ­5π/6
Use your special angles on the unit circle to find two values of θ between 0 and 2π that satisfy each of the following:
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