* The   strategy   used   depends   upon   the   given   information   in   the   problem.
METHOD   #1
Numeric   value   of

is   given   AND

is   a   common   angle.
A.

not   Quadrantal   angle   a.
Draw

on   Unit   Circle   b.
Identify   reference   angle   c.
Draw   right   triangle   d.
Label   (triangle   (remember   +/ ‐ )   e.
Evaluate   trig   fns.
B.

is   Quadrantal   angle   a.
Draw

on   Unit   Circle   b.
Label   (x,y)   point   on   circle   c.
sin

=   y   and   cos

=x
d.
Use   these   to   evaluate   other    e.
trig   fns.
Ex.
Evaluate   sin135

Ex.
Evaluate    cos

METHOD   #2
Numeric   value   of

is   NOT   given.
Instead   coordinates   of   point   P   on   terminal   side   of

are   given   –   OR   –   a   particular   trig   function   value   and   quadrant   of

are   given.
a.
Draw   point   P   in   XY   plane.
Draw   angle

through   point   P.
b.
Draw   right   triangle   by   connecting   point   P   to   x ‐ axis   with   a   right   angle.
c.
Label   sides   of   triangle   using   the   coordinates   of   point   P.
d.
Use   Pythagorean’s   Theorem   to   find   the   value   of   the   hypotenuse.
e.
Now   that   all   3   sides   of   triangle   are   known,   use   the   triangle   to   evaluate   the   trig   functions.
Ex.
Let   P   (3,  ‐ 5)   be   on   the   terminal   side   of

.
Evaluate   the   trig   functions   at

.
Ex.
Given   that   sin
 
3
and
5

is   in
Quadrant   1,   evaluate   trig   functions   at

.
METHOD   #3
Numeric   value   of

is   given   but

is   NOT   a
common   angle.
a.
Check   mode   on   your   calculator.
Set   to   appropriate   mode.
b.
Use   calculator   to   evaluate   the   trig   function.