Mathematical Investigations III
Name
Mathematical Investigations III
Trigonometry- Modeling the Seas
RECIPROCAL FUNCTIONS & SPECIAL VALUES
1.
Find the lengths of the remaining sides of each pair of similar triangles. (Not to scale!)

1
30o
1
30o

1
45
1
o
45o
In a triangle in standard position (with a radius as hypotenuse) within the unit circle, the
opposite
y coordinate is equal to sin( ) . In other triangles, we have sin( ) 
. By this
hypotenuse
definition, trigonometric functions depend on , not on the size of the triangle or the circle.
2.
Use the information in the above triangles to complete the following table.
 (radians)
0
/6
/4
/3
/2
/3
/2
 (degrees)
sin()
cos()
tan()
3.
Use the table above to complete the following table.
0
 (radians)
/6
/4
cot()
sec()
csc()
Trig. 10.1
Rev. S05
Mathematical Investigations III
Name
4.
Find exact values for each of the following.
 3 
 2 
a. sec  
b. cot  
 4 
 3
  
c. sec 
 2 

d. cot  
 3
 5 
e. csc 
 4 
 7 
f. cot 
 2 
 7 
g. csc  
 6 
  
h. sec 
 6 
 5 
i. csc  
 3
 19 
j. cot 
 6 
 3 
k. csc  
 2 
 2 
l. sec 
 3 
3
and sin( )  0 , find the value of each of the six trigonometric functions of .
5
5.
If cos( )  
6.
Find the value of all 6 trig functions of  .

(8, 15)
7.
If tan   
1
and cos    0 , find the values of each of the trig functions of  .
4
Trig. 10.2
Rev. S05