Q: Find two vectors v and w such that the three vectors u = (1,-1,-1), v and w are linearly independent independent.
Month: October 2009
Going backwards?!
Q: Express sin9x – sin7x as a product containing only sines and/or cosines:
A. 2sinx cos8x
B. -2sinx cos8x
C. 2sin8x cos x
D. -2sin8x cosx
Rationalizing the Denominator
More Trig Identities!
Q: Factor the expression and use the fundamental trigonometric identities to simplify:
cos²x sec²x -cos ²x =
A. cos²x cot²x
B. cos²x
C. 1
D. sin²x
Exact Values using identities
Product-to-sum Identity Example 2
Q : Which is 2*sin(4x)*cos(2x) written as a sum containing only sines?
A. sin 6x – sin 2x
B. sin 5x – sin3x
C. sin 5x + sin 3x
D. sin 6x + sin 2x
Product-to-Sum Identity
Q: Which of the following expresses 2cos(5x)* cos(2x) as a sum containing only sines or cosines?
A. cos(7x)-cos(3x)
B. cos(6x)+cos(4x)
C. cos(7x)+cos(3x)
D. cos(6x)-cos(4x)
Identities to Memorize
Q: Which expression completes the fundamental trigonometric identity ? sec(-x)
A. -sec x
B. sec x
C. cos x
D. -cos x
Double Angle Identity
Q: Find the exact value of sin(2a) and cos(2a) using the double angle formulas, given sin(a) = 5/9 , π/2 < a < π
Trig Identities
Q : Which expression completes the fundamental trigonometric identity sin(π/2-u) =
A. -sec u
B. csc u
C . cos u
D. -sin u
