MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.12.htm © 2025   A2, Agnes Azzolino Angles and their measures, Text 7.1 , PG. 576

Welcome to Precalc! Much of Today's Work You Probab ly Already Know. Hi,     Print for this class "3., 4. pdf of 30-60-90 and 45-45-90 triangles and trig functions of 30°, 60°, and 45° angles" found at Spring 2020 Trig Note Sheets and Connect-the-Dots at the bottom of the course home page.     Before class starts, look over the vocabulary listed & linked below to determine if you need a review of any word.         Contact me through the pink box on www.mathnstuff.com/math/math.htm or with the phone number on your class CANVAS home page.     Stay safe, A2

7.1  - pg 576,  Learning Objectives
* Draw angles in standard position.
* Convert between degrees and radians.
* Find coterminal angles.
* Find the length of a circular arc.
* Use linear and angular speed to describe motion on a circular path.

radius circle chord parts of a circle

concentric inscribed vertical angle

central angle arc major arc minor arc radian IN MATH, standard position IN PHYSICS, standard position

Support
• complement, supplement gsp   -- just complementary & supplementary angles
• sine.gsp   -- just right triangle sine
• cosine.gsp   -- just right triangle cosine
• tangent.gsp   -- just right triangle cosine
• standardPosition.gsp
  1 standard position angle central angle, negative & positive angle measures
  2 angles coterminal?
• radianSector.gsp
  1 intro angles degrees radians
  2 radian questions
  3 arc length angular speed sector area
  4 sector and area
• veronica.gsp
  1 - 1 standard position angle
  2 - angles coterminal?
  3 - 1 veronica angles -- trig fx of angles is 4 quadrants
  4 - 2 veronica angles
  5 - extra 2 veronica angles
• Veronica's Bow Tie pdf
• 3 trig planes image
• elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant

11. Circle's arcs and sectors from the function & computation page     Though radians make these formulas MUCH easier and clearer, this part of the page uses only degrees to measure angles and builds the conversion from degree to radian into the formulas. In the list of units shown below and the other images, the conversion formula is visible. The radians page also has a calculator to convert from radians (based on a circle's angle measure of 2 ) to degrees (based on a circle's angle measure of 360°).     For the full story, see Arc Formulas and Rational, and Sector Formulas and Rational.     Click on the image below to see an enlargement of the formulas that are used here. Input the data. radius = central angle measure in degrees = time (if needed) = Press button to obtain the computed measure. arc length, s, units of length linear speed (unit of length)/(unit of time) angular speed degrees/(unit of time) area of sector square units