4.2 trigonometric function: the unit circle. the unit circle a circle with radius of 1 equation x 2...
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Do you remember 30º, 60º, 90º triangles?
Now they are really! Important
Even more important
Let 2a = 1
Do you remember 45º, 45º, 90º triangles?
When the hypotenuse is 1
The legs are 2
2
2
245
2
245
Sin
Cos 1
2
2
2
2
Some common radian measurements
These are the Degree expressed in Radians
360
445
630
23602
3270
1802
90
The Six Trig functions
adjacent
opposite
b
aTan
hypotenuse
opposite
c
aSin
hypotenuse
adjacent
c
bCos
CotTan
CscSin
SecCos
tan
1sin
1cos
1
Cos
SinTan
Why does the book use “t” for an angle?
Since Radian measurement are lengths of an arc of the unit circle, it is written as if the angle was on a number line.
Where the distance is “t’ from zero.
Later when we graph Trig functions it just works better.
Lets find the Trig functions if
Think where this angle is on the unit circle.
3
2
3
21
23
3
2
2
3
3
2
2
1
3
2
Tan
Sin
Cos
3
2
Cos
SinTan
2
3,
2
1
Find the Trig functions of
Think where this angle is on the unit circle.
3
21
23
3
2
2
3
3
2
2
1
3
2
Tan
Sin
Cos
3
2
3
3
3
1
3
2
3
32
3
2
3
2
21
2
3
2
Cot
Csc
Sec
If think of the domain of the trig functions, there are some limits.
Look at the unit circle. If x goes with Cos, then what are the possible of Cos?
It is the same with
Sin?
Definition of a Periodic Function
A function “f” is periodic if there exist a positive real number “ c” such that
f(t + c) = f(t) for all values of “t”.
The smallest “c” is called the period.
Even Function ( Trig. )
Cos (- t) = Cos (t) and Sec( -t) = Sec (t)
Also
Sin(-t) = -sin (t) and Csc (-t) = - Csc (t)
Tan(-t) = -Tan (t) and Cot(-t) = - Cot (t)
HomeworkHomework
Page 278- 279 Page 278- 279
##1, 5, 9, 13, 17, 1, 5, 9, 13, 17,
21, 25, 29, 33, 21, 25, 29, 33,
37, 41, 45, 48, 37, 41, 45, 48,
52, 59, 6852, 59, 68
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