1-16-2025

Last updated 8 months ago

6 questions

Do Now

Do Now- You are given the angle 500\degree . 

Solve for a co terminal angle  \theta such that 0<\theta<360

\theta=_______ 

With the given information, what is the reference angle for \theta? _______

Measuring a Circle

Instead of over complicating things, let's image a circle with a radius of 1. (leave your answer as a simplified fraction \frac{5\pi}{6})

What is the Circumference of the full Circle? _______ 

What is the Circumference (Arc Length) of half a Circle?_______ 

What is the Circumference of a third of a circle? _______

Converting

Teacher Example: Convert \frac{5\pi}{6} to degrees

Student Example \frac{8\pi}{3}

Teacher Example: Convert 15 degrees to radians

Student example: Convert 275 \degree to radians.

Coterminal and Reference Angles

It helps to have the angles measured in radians instead because it helps with solving arc length and area of a sector. The formulas are simpler and more concise. 

Find an angle \theta that is co terminal to \frac{-2\pi}{7} where 0\leq \theta \leq 2\pi

What is the reference angle for \frac{4\pi}{3} 

_______ 

What is the reference angle for \frac{5\pi}{3} 
_______ 