Mathematical Investigations IV
Name:
Trigonometry - Beyond the Right Triangle
An Opportunity to Demonstrate Knowledge (Form α)
Instructions: Answers without work will receive little or no credit. You must show sufficient
work on all problems so that I can reproduce your results. If any problem has multiple
solutions, be sure you clearly indicate which values go together. You may use a TI-30 on this
exam.
8
12
, cos   0 , cos   , and sin   0 , find the exact values of the following.
17
13
a) sin    
b) csc(2 )
1)
If sin  
2)

 3 
Find a simplified expression for csc  tan 1    .
 x 

3)
Find the area of the triangle.
29
48
10
Mathematical Investigations IV
Name:
4)
Find the equation for the function graphed below.
5)
Give all solutions to the following equations using radians. Give exact values when
possible.
a) cos 2x  5cos x  3  0
b) sin 2   cos 2   1  cos 
Mathematical Investigations IV
6)
Name:
Solve the triangle by finding the remaining sides and angles. Give your answers to the
nearest hundredth.
In PQR, Q = 39°, q = 43, and p = 51.
7)
In XYZ, with X = 38°, and y = 14, what are the possible values for the length of side x that
will give exactly one triangle?
8)
Simplify the following trig expression:
sin    cos    cot  
cos  2   2 cos 2  
Mathematical Investigations IV
Name:
9)
4. In Parallelogram ABCD,
AC  12 , BD = 16, and
AEB  130o
A
Find the perimeter of ABCD
to the nearest hundredth.
E
D
10) Prove:
sin    
 tan   tan 
cos  cos 
B
C
Mathematical Investigations IV
11)
a)
b)
Name:
Do one of the following:
Derive the formula: tan(a  b  c) 
tan a  tan b  tan c  tan a  tan b  tan c
1  tan a tan b  tan a tan c  tan b tan c
2
x  3 , and a third line intersect to form an
5
isosceles triangle in the first quadrant. If the third line passes through the origin, find the
equation of the line.
The graphs of the lines y  3x  3 , y 
Mathematical Investigations IV
Name:
n
12)
13)
1

Consider  2 x   . For what values of n will there be a term in the expansion that is
x

constant, that is, has no x in the term? Justify your answer.
sin( x) 
4 3
x
,   x  2 . Find sin   .
5 2
2