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4.2 Trigonometric Functions (part 2)
III. Trigonometric Functions.
A) Basic trig functions: sine, cosine, tangent.
B) Trig functions on the unit circle: finding (x , y).
1) sine finds the height (y coordinate) on the unit circle.
2) cosine finds the width (x coordinate) on the unit circle.
a) Think alphabetical order: (x , y)  (cosine , sine).
3) If you know one of the coordinates (say x), you can find
the other coordinate (this would the y) by using tangent.
C) Other trig functions: cosecant, secant, cotangent.
1) cosecant = 1/sine
(abbreviated csc)
2) secant = 1/cosine
(abbreviated sec)
3) cotangent = 1/tangent (abbreviated cot)
a) To find these, find the x (or y) value and flip it.
4.2 Trigonometric Functions (part 2)
IV. Things the book does to confuse you.
A) Instead of saying the angle is θ, they call it t.
1) They write sin t = y instead of sin θ = y.
a) What they want is the y coordinate at θ.
2) They write cos t = x instead of cos θ = x.
a) What they want is the x coordinate at θ.
3) In other words, find the (x , y) coordinates on
your unit circle for the angle θ and either tell
them the x coordinate (for cos) or the
y coordinate (for sin) at the angle.
4.2 Trigonometric Functions (part 2)
V. Even and Odd Trigonometric Functions.
A) To determine if a function is even or odd, change the x’s
to –x’s and simplify (determine the sign of each term).
1) It is EVEN if you get the original function.
2) It is ODD if you can factor out a -1 and that gives you
the original function.
B) Even trig functions: cosine and secant.
1) cos (-t) = cos t
and
sec (-t) = sec t
C) Odd trig functions: sine, tangent, cosecant, & cotangent.
1) sin (-t) = - sin t
and
tan (-t) = - tan t
csc (-t) = - csc t
and
cot (-t) = - cot t
4.2 Trigonometric Functions (part 2)
VI. Domain and Period of Sine and Cosine.
A)
t
The arc length (t) corresponds to the angle θ.
1) The t is the domain (the θ).
2) Since the angle, θ, can be + or – and go around and
around the circle as many times as it want too, the
domain is all real numbers.
B) The range is the height of the graph (the y coordinate) on
the unit circle.
1) The graph goes from -1 to 1. So range is -1 < y < 1.
4.2 Trigonometric Functions (part 2)
VI. Domain and Period of Sine and Cosine.
C) The graph of sine and cosine look like waves.
D) The period is how far the graph goes before it
repeats itself.
1) sine and cosine repeat every 2π (or 360°).
HW: page 299 # 5 – 28 all