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: cos1 (.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.