An even function is symmetric with respect to the yaxis' For any x value plugged into the function,

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An even function is symmetric with respect to
the y-axis. For any x value plugged into the
function, you get the same height or function
value as you do if you plugged in the negative
version of x. The function on the right is an
example of an even function.
Examining a table of function values can lead
to this conclusion. For even functions f ( x )
f ( -x )
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An odd function is symmetric with respect to
the origin. For any x value plugged into the
function, you get the opposite height or function
value as you do if you plugged in the negative
version of x. The function on the right is an
example of an odd function.
Examining a table of function values can lead to
this conclusion. For odd functions f ( -x )
-f ( x )
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Odd or Even?
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Odd or Even?
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Of the six trigonometric function, 2 are even and
the other 4 are odd. Even Odd Cos (x)
Sin (x) Csc (x) Sec (x) Tan
(x) Cot (x)
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RememberFor even functions
For odd functions f ( x ) f ( -x ) f (
-x ) f ( x )

• E1.) Find sin (-t) if sin (t) 1.
• Since the sine function is odd, f ( -x )
  f ( x )
• sin ( -t) sin ( t )
• sin ( -t) ( 1 )
• sin ( -t) 1
  
• E2.) If cos (t) ¾, find cos (- t) and find sec
  (-t).
• Since the cosine and secant functions are both
  even, f ( x ) f (- x )
• cos (x ) cos (-x ) sec (x ) sec (-x )
• cos ( t ) cos ( -t ) sec ( t ) sec ( -t )
• ( ¾ ) cos ( -t )
• ( 4/3 ) sec ( -t )

sec (-t)
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• E3.) Given cos (t) 4/5, find
• a.) b.)
• Lets look at the unit circle to draw a
  conclusion about these two questions.

• a) Cosine values are given by the x-coordinate
  on the unit circle. Lets say that t p/6,
• so .
• is really just finding
  the cosine at the supplement, or, cos 5p/6 which
  is the same value only negative.
• I could say that cos (p-t) is the same value as
  cos (t) only negative so cos (p-t) - 4/5.
• Cos ( t 6p ) is easier to evaluate. If I know
  that cos ( t ) 4/5, and I take my angle t and
  add 6p to it, that would be like going around the
  circle 3 more times and winding up in the same
  spot again. Remember, adding or subtracting
  multiples of 2p doesnt change the value of a
  trig function.
• So, cos (t) cos (p-t) 4/5

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• E3.) Evaluate sec 35 on your calculator.
• Sec 35 1.221
• E4.) Evaluate cot 15 on your calculator.
• cot 15 -1.168

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6 Trig Functions with Right Triangles

• Sin ? opp/hyp
• Cos ? adj/hyp
• Tan ? opp/adj
• Csc ? hyp/opp
• Sec ? hyp/adj
• Cot ? adj/opp

• hypotenuse
  opposite
  ? adjacent

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E5.) Find the 6 trig function of this right
triangle. ? 3 1
First find the 3rd side by the pythagorean
theorem.