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.
Vocabulary
ray
vertex
angle
adjacent
supplementary
complementary
right angle
acute
obtuse
straignt angle
reflex angle
triangle
equilateral
isoscele
scalene
congruent
similar
degree
minute
radian
sine
cosine
tangent
secant
cosecant
cotangent
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
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.
  1. radius =
  2. central angle measure in degrees =
  3. time (if needed) =
    Press button to obtain the computed measure.
  1. arc length, s, units of length
  2. linear speed (unit of length)/(unit of time)
  3. angular speed degrees/(unit of time)
  4. area of sector square units