Trigonometry Review

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Trigonometry Review
What you need to know for Calculus
BY Janelle Montemayor
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Radians VS Degrees

• p 180 Degrees
• 2p in a circle
• 360 Degrees in a circle
• Conversions
• Degrees to radians multiply by
  
• Radians to degrees multiply by

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90
60
120
45
135
30
150
Conversions You Should Know
p
0, 2p
0,360
180
330
210
225
315
300
240
270
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Sectors of Circles
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The sector of an area is the region bounded by a
central angle and the intercepted one. If the
central angle of the sector is 60 and the radius
is 12, then the arc length of the sector is of
the whole circumference, or (2pr 12)4p.
The area of the sector is of the area of the
whole circle, or 2
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General Formulas S is arc length K is area of
circle If is in degrees, then s
K 2 If is in radians,
then s r K 2
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Trig. Functions
Domain All Real Numbers Range -1 lt Y lt 1
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Trig. Functions
Domain All Real Numbers Range -1 lt Y lt1
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Trig. Functions
Domain All Real Numbers Except Odd Intervals
of .
Range All Real Numbers
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Special Triangles

• 
  
  

2
1
1
1
45-45-90 Triangle
30-60-90 Triangle
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Evaluating Sin, Cos, and Tan
2
2
2
1
1
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Graphing Trig. Functions
Y A Sin Bx and Y A cos Bx
(A 0 and B gt 0) Amplitude A
period
Standard Shape
Sin Graphs start at Y0 Cos Graphs start at
Y1 If the graph is to be translated
horizontally h units and vertically k units, then
the resulting graph is The same goes for the
graph.
By changing the values of k and h, you can
stretch or shift the graph. This will also change
the period of the graph.
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Graph Transformations

• If the equation yf(x) is changed to
  Then the graph of yf(x) is

Y-f (x) Y f (x)
Reflected in the x-axis Unchanged when f (x)gt0
and reflected in the x axis when f
(x)lt0 Reflected in the y-axis Reflected in the
line yx Stretched vertically Shrunk
vertically Shrunk horizontally Stretched
horizontally
Y f (-x)
Xf (y)
Y cf (x), cgt1
Y cf (x), 0ltclt1
Yf (cx), cgt1
Yf (cx), 0ltclt1
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Trig. Functions
Domain XAll Real Numbers. X multiples of
p. Range Y -1lt Y lt 1 Domain XAll Real
Numbers X multiples of p Range -1lt Y lt
1 Domain XAll Real Numbers X multiples of
p Range YAll Real Numbers
2
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Inverse Trig. Functions

• Inverses are the ordered pairs of their
  corresponding functions, reversed.
• Inverses functions are FUNCTIONS, so they must
  pass the vertical line test. For this reason,
  only a portion of the original function is used
  to find the inverse.

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Sin-1(X)ArcSin(X)
Domain -1 lt X lt 1
Range lt Y lt
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Cos-1(X) ArcCos(X)
Domain -1 lt X lt 1 Range 0 lt Y lt p
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Tan-1(X)ArcTan(X)
Domain lt X lt
Range lt Y lt
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Other Notes
Sin2 Cos2 1 Sin , Csc , Tan
, Cot are all odd functions. Cos
Sec are even functions. Even means f(-x)
f(x). Odd means f(-x) -f(x)
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• This concludes the show.
• Hopefully, you have been given a basic review of
  trig. which will help you in the coming year.