Mathematical Investigations IV
1.
Trig Quiz
Name: _________________
3

1

If cos   ,     0, and sin   , 0    , find the exact values of the
5
2
3
2
following:
a) sin 
b)
cos 
c) sin  2 
d) sin    
2. Solve for x: cos(3x  .65)  .7 (Note: cos1 (.7)  2.35 )
3. Find the period of f ( x) 
cos(2 x) sin(2 x)

sec(4 x) csc(4 x)
Mathematical Investigations IV
4. Solve for x:
Trig Quiz
Name: _________________
3
1
2
cos x  sin x 
2
2
2
5. a. Find and simplify the matrix which rotates points in the plane through an angle 30 in the
counter-clockwise direction about the origin. Call this matrix A.
0 1 
b. Let B  
 . Explain with a complete sentence or two what geometrical transformation
1 0 
the matrix B represents.
c. Find A  B and B  A .
d. Explain with complete sentences why the result in c. makes sense geometrically.
This makes sense that multiply in a different order gives a different matrix. If you think about
reflecting over the line y = x then rotating, you will not get to the same spot as if you rotate
first, then reflect over the line y = x.