1. Additional Topics in math Lessons 5-7
Degree, Radians, and Arc Length
The Unit Circle and Trigonometric Functions with Radian Measure
Circle Definitions and Equations
Simplification of Imaginary Monomial Expressions
Arithmetic Operations on Complex Numbers

2. Degrees, Radians, and Arc Length
Angles can be measured in degree or radians
We are used to degrees but trigonometry uses radians
A Circle = 360°
A Circle = 2π
To convert degrees to radians you multiply by π/180
To convert radians to degrees you multiply by 180/π
This can be done by replacing the π with 180
Arc Length: s = θr or l = θr BUT… θ must be in radians!

3. The Unit circle and trigonometric functions with radian measure
You need to know where the sin, cos, and tan functions are positive and negative
Use “All Students Take Calculus” to help you remember where the trig functions are positive.
You will need to use reasoning to identify where they are negative
Students
Sin +
All +
Take
Tan +
Calculus
Cos +

4. Circle definitions and equations
Equation of a circle: (x – h)2 + (y – k)2 = r2
When finding h and k remember to change the sign
(h, k) is the center of your circle
r is your radius but remember to square root r2 to get r
The radius can be found by finding the distance from the center to a point on the circle
If a point is ON the circle then the x and y from that point must make the equation true

5. Simplification of imaginary monomial expressions
The imaginary number “i” allows us to square root negative numbers
You simplify the root as you would a positive number then include “i” in your answer
The exponents of “i” follow a pattern:
i = i i5 = i
i2 = -1 i6 = -1
i3 = -i i7 = -i
i4 = 1 i8 = 1
So if you remove all the multiples of 4 from the exponent you can simplify even large exponents

6. Arithmetic operations on complex numbers
When performing operation with “i” – treat it as you would any other variable
When simplifying you must not leave i2 anywhere: i2 = -1
To Add/Subtract Complex Numbers – Combine Like Pieces
To Multiply Complex Numbers – FOIL and clean up
To Divide Complex Numbers – Multiply both the top and bottom by the conjugate of the denominator
A Conjugate of a binomial changes the middle sign
Example of Conjugates: i and 3 – 2i