Transcript Reciprocal Trig

What is the length, x, of
your shadow as you walk
to the right and the angle,
, to the lamp decreases?

x
What is the length, x, of your
shadow as you walk to the right
and the angle, , to the lamp
decreases?

x

x

x
Assume you
are 2m tall:
Opp 2
tan 

Adj x
2

x
Assume you
are 2m tall:
Opp 2
tan 

Adj x
2
x 
tan( )
2

x
6
4
I can picture the
relationship between 
and tan().
2
0
-90
-60
-30
0
-2
-4
-6
30
60
Angle90
But what does
1/tan()
relationship look
like?
6
1/tan()
1/tan() looks like
this, and is called
the cotangent.
4
2
0
-90
-60
-30
0
-2
-4
-6
30
60
Angle90
Notice as the angle gets closer
and closer to zero, the length
of your shadow approaches
infinity.
18
So 2/tan() looks like this.
When the angle is 90,
14
you have zero shadow;
when the angle is 45, you 10
have a shadow of 2m,
when the angle is 15,
6
your shadow is approx
20m long.
2
-90
-60
-30
-2 0
-6
2*cot =2/tan()
Assume you
are 2m tall:
tan  
Opp 2

Adj x
2

x
Angle
30
60
90
Reciprocal of a line
Notice how like any reciprocal function, all values of the function
in the band ‘0 to 1’ get stretched to the ‘greater than one band’; all
values greater than one get compressed into the ‘zero to one’ band.
Same for the negative bands too.
You can survive without cotangent, and
secant, and cosecant. But their graphs
make picturing typical problems in
daily life easier.
In fact you can survive with only ‘sine’
if necessary, all the other trigonometric
functions are just for you to better
picture relationships between angles
and some other related value.