Precalc Chapter 6

Ambiguous Cast Test for ASS

1. Solve first triangle, if possible

2. 180 — first angle found

3. add the given angle

4. compare the sum to 180

5. If smaller than 180, then 2 triangles, if equal to 180, then 1 triangle. If greater than 180, then no triangle.

Law of cosines, how to get a side…

a² = b² + c² - 2bc CosA

b² = a² + c² - 2ac CosB

c² = a² + b² - 2ab CosC

Law of Cosine, how to get an angle

cosA = b² + c² - a² / 2bc

cosB = a² + c² - b² / 2ac

cosC = a² + b² - c² / 2ab

How to solve SSS triangle

1. find the angle opposite the LONGEST SIDE FIRST

2. Use law of sines to find missing angles

3. find third angle, (together must equal 180)

How to solve SAS triangle

1. find the side opposite the given angle

2. find angle opposite the shorter of the two given sides

3. find third angle

Heron’s Formula (how to find semi perimeter)

s = 1/2(a+b+c)

how to find component form of a vector

{x2 - x1, y2 - y1}

how to find magnitude

√a²+b²

how to find direction angle

tanx= b/a

unit vector (magnitude of 1)

u = 1/IIvll * v

trigonometric form of a unit vector

<cosx, sinx>

trigonometric forms of any vector

llvll <cosx, sinx>

dot products

a1 * a2 + b1 + b2

finding magnitude by using dot product

llvll = √v * v

how to find angle between two vectors

cosx = v * w/ llvll llwll