*7-5 The Four Other
Trig
Functions*

*The following are
the
defintions of the other 4 trig functions*
*tangent of q:
tan q = y/x*
* *
*cotangent of q:
cot q = x/y*
*secant of q:
sec q
= r/x*
*cosecant of q
: csc q = r/y*

*These four trig
functions
can be written in terms of sin and cos of q*
*The last one shows
that
the cotangent and tangent are reciprocal functions. Secant and
cosine,
as well as Cosecant and sine are reciprocal funtions.*

*It is easy to
memorize
the signs of the six trig functions. All are positive in Quad I,
Sine and Csc are positive in quad II, Tan and Cot are positive in Quad
III, while Cos and Sec are positive in quad IV.*

*Graphs of the other
trig
functions:*
*Tangent graph:*
Demonstration
of the Tangent Graph (Manipula Math)
*Period length is p*
*zeros at 0, p,
2p*
*undefined at p/
2, 3p / 2*
*This corresponds to
the
zeros of sin -- this is where the tangent crosses the x-axis, and*
*to the zeros of the
cos
-- this is where the tangent is undefined.*

*Cotangent graph:*
*Period length is p*
*zeros are at: p/
2, 3p / 2*
*undefined at: 0, p,
2p*
*This again
corresponds
with the zeros of the sine and cosine, simply reversed from the tangent
graph.*

*Secant graph*
*The blue
graph is the secant graph. We can generate the secant graph by
knowing
the graph of the cosine. Remember that they are reciprocal
functions.
When the cosine is zero, the secant is undefined. When the cosine
is at a maximum value, the secant is a minimum. When the cosine
is
at a minimum, the secant is a maximum.*
*Period length is 2p*
*Keep in mind that
when
a graph is undefined, there is a vertical asymptote.*

*Cosecant Graph:*
*The blue
graph is the cosecant graph. This graph has the same relationship
to the sine graph that the cosine and secant graph had.*
*Period length is 2p*

*Example problems*
*1) Find the other
trig
functions if sin q = 3/5 and q
is in quadrant II.*

*
y = 3, r = 5, therefore x = -4. Negative because we are in quad II*

*
cos q = -4/5*

*
tan q = -3/4*

*
csc q = 5/3*

*
sec q = -5/4*

*
cot q = -4/3*
*2) Find each of
the
values for the trig functions using your Ti-82 graphing
calculator.
Round to 4 significant digits.*

*
a) Tan 115*^{o}

*
Make sure you are in degree mode. Type*

*
tan 115. Answer -2.145*

* *

*
b) Cot 95*^{o}

*
Since cot and tan are reciprocals and you don't have a cot button, type
it in as:*

*
1/tan 95 -----> Answer -.0875*

* *

*
c) Csc 5*

*
Make sure you are in radian mode.*

*
since we don't have a csc button but we remember that csc is the
reciprocal
of sin, type it in as:*

*
1/sin 5 -----------> Answer: -1.043*

* *

*
d) Sec 11*

*
Since sec and cos are reciprocals, type as:*

*
1/cos 11 ---------> Answer: 226.0*

**That's
it for this section. Let's head into the last section on inverses.**
**Go
for it!!**
**I
can't go on!! I am completely lost!! Take me back!**

* *