Pre Calculus 2 Things to Remember

This is a Knowt based on important things to remember for the Pre Calculus 2 final exam.

Gaussian elimination matrix

Work down and to the right

Gauss-Jordan elimination matrix

Work up and to the left

How do you change a number in a matrix into a 1?

Multiply a row by a nonzero constant (½ R₃)

How do you change a number in a matrix into a 0?

Add a multiple of one row to another (2R₁ + R₂)

What is another way to change a row in a matrix?

Interchange 2 rows ( R₁ ←→ R₂)

When can you add or subtract matrices?

When they have the same dimensions

When can you multiply 2 matrices?

When they have the same inner numbers for their dimensions (2 × 2 & 2 × 3 → the inner 2s are the same, so matrix will be 2 × 3)

How do you find the inverse of a 2 × 2 matrix?

How do you find the inverse of a non 2 × 2 matrix?

-Mirror it with Gauss-Jordan elimination

-Solve it until the left side looks like Gauss-Jordan elimination

How do you find the determinant of a 2 × 2 matrix?

det (A) = ad - bc

Cramer’s Rule formulas

x = Dx/D & y = Dy/D

Acronym for Trig Functions

SOHCAHTOA

Period Formula

Per = 2π/B

y = AsinB(x-c) or y = AcosB(x-c) (Horizontal shifts)

• x - c → shift right (→)

• x + c → shift left (←)

y = AsinB(x-c) + D or y = AcosB(x-c) + D (Vertical shifts)

• D > 0 → shift up (↑)

• D < 0 → shift down (↓)

When you have both horizontal and vertical shifts, what shift should you do first?

Horizontal, then vertical

Arc Length, s

s = rθ

-r = radius, θ = central angle (in radians, NOT degrees)

Area of a sector, A

A = ½ r² θ

Linear speed, v

v = s/t = arc length/time

Angular speed, w

w = θ/t = central angle (rads)/time

Where does inverse sin exist?

In Q1 & Q4, -π/2 ←→ π/2, -90° ←→ 90°

Where does inverse cos exist?

Q1 & Q2

Where does inverse tan exist?

Q1 & Q3

Trig Identity 1

tan θ = sin θ/cos θ = 1/cot θ

Trig Identity 2

cot θ = cos θ/sin θ = 1/tan θ

Trig Identity 3

sin² θ + cos² θ = 1

Trig Identity 4

1 + tan² θ = sec² θ

Trig Identity 5

1 + cot² θ = csc² θ

Trig Identity 6

a (b-c) = ab - ac

Trig Identity 7

a² - b² = (a-b)(a+b)

What should you do with original angle when using double-angle formulas?

Divide it by 2

• cos 270 = cos 2u = cos 2 (135) → u = 135

What should you do with original angle when using half-angle formulas?

Multiply it by 2

• sin 75 = sin u/2 = sin 150/2 → u = 150