**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

## Product to Sum Trig Identity

**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

**Q: Rationalize the denominator:**

**[√(x) +1 ]/ [√(x) – 3 ]**

## 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

**Q: Find the exact values:**

** (a) sin(5π/12)**

**(b) cos(5π/12)**

**(c) tan(5π/12)**

## 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**

## Proof by Induction

## Parabolas

**Q: Consider the quadratic equation: y = 2x² -14x + 20:**

**(a) Put the equation in general form & find the vertex
**

**(b) Put the equation in standard form & find the vertex**