4.4 --> Trigonometric Functions of Any Angle
Positive Trigonometric Values
Sine &
Cosecant
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All
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Tangent & Cotangent
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Cosine & Secant
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"All Students Take Calculus"
All are positive in Quadrant I
Sine and Cosecant are positive in Quadrant II
Tangent and Cotangent are positive in Quadrant III
Cosine and Secant are positive in Quadrant IV
Ex) Point (1, ) is on the terminal side of an angle. SIN > 0, COS > 0. Find the six trigonometric ratios and name the quadrant.
Both SIN and COS are positive, so the triangle should be drawn in...Quadrant I
sin()= cos()=1/2 tan()= csc()= sec()= 2 cot()=
Reference Angle - Angle formed between the terminal side of an angle and the X-Axis
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Always Acute
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Always Positive
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Alpha () or Theta Prime (')
Ex) Find Reference Angle
A. = 186°
- Nearest X-Axis = 180°
- = 6°
B. = 91°
- Nearest X-Axis = 180°
- = 89°
C. = 285°
- Nearest X-Axis = 0°
- =75°
Exact Values...
Ex) Cos 150 = ?
Step 1: Find the Refence Angle Nearest X-Axis = 180°, = 30°
Step 2: Cos 30° =
Ex) Cos 0° = ?
Step 1 --> Find point on Unit Circle --------> Point at (1,0)
Step 2 --> Find 6 Trigonometric values
Sin = Y/R --> 0
Cos = X/R --> 1
Tan = Y/X --> 0
Csc = R/Y --> 0
Sec = X/R --> 1
Cot = X/Y --> 0
Ex) Find two values of that satisfy Sin = .6
Step 1 --> Find ArcSin .6 = 36.87°
Step 2 --> Pick Quadrants Sin Positive in Quadrants I & II
Step 3 --> Subtract value from 180° Values = 36.87°, 134.13°
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Comments (1)
Anonymous said
at 8:37 pm on Jan 8, 2008
Looks great! 20/20
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