Law of Sin/Cos + The Complex Plane - Unit 6 HPreCalc

Heron’s Formula

Area of a triangle

Law of Sines

AAS, ASA, ASS (donkey/special case)

Law of Cosines

SAS or SSS

What is h

Use h’s relation to a and b to determine the number of triangles. (for acute triangles)

When are there 2 triangles

h < a < b when an acute triangle

• only occurs in an acute triangle

When is there 1 triangle

• When a > b in an obtuse triangle

• when a = h, a > b, or a = b in an acute triangle

When are there no triangles

• obtuse a < b or a = b

• acute: a < h

What to do when asked to solve a triangle

The complex plane

Distance Formula

Trigonometric Form

z is the point. to convert back, rewrite the cos and sin in their ratios, then distribute r

Multiply Complex Numbers

Divide Complex Numbers

What form should your answer be in?

whichever form it is given to you in

Powers of complex numbers

roots of complex numbers

there are n roots with k=0,1,2,… n-1

• multiple solutions

graphing roots of complex numbers

They are all the same distance apart

• this a a cube root