MathematicsChapter 6: Trigonometry and Bearing
Sexagesimal Measure
Everyday angles in this book use the sexagesimal English degrees system.
Learning objectives
- Explain sexagesimal measure in clear mathematical language
- Apply the ideas in degrees minutes seconds
- Solve problems involving other systems
Definition
Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec. A right angle is 90 deg, a straight angle is 180 deg, and a full turn is 360 deg. Centesimal measure (grades) exists in some older books but is beyond this book. Circular measure uses radians and is the other system you must convert.
Formula
deg = 60 min
Where / symbols
- sexagesimal
- Everyday angles in this book use the sexagesimal English degrees system.
- English degrees
- Everyday angles in this book use the sexagesimal English degrees system.
- 1 deg = 60 min = 3600 sec
- Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec.
- Centesimal
- Centesimal measure (grades) exists in some older books but is beyond this book.
Relationship
- 1 deg = 60 min = 3600 sec
Overview
Degrees for drawing; radians for the circle:
Degrees Minutes Seconds
In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec. A half degree is 30 min. When you add angles, 60 min become 1 deg, just as 60 seconds become 1 minute on a clock. Keep the three units lined up when you add or subtract.
Examples 90 deg is a right angle · 30 min is half of 1 deg · 1 deg 30 min = 1.5 deg
Other Systems
Centesimal measure divides a right angle into 100 grades. The course tells you it is beyond this book, so do not mix grades with degrees in an exam answer. Circular measure uses radians: the angle is the arc length divided by the radius. You will need both degrees and radians, and the link between them, on the next page.
Examples Degrees: 90, 180, 360 · Centesimal: mentioned, not used here · Circular: radians on a circle
What it means
Everyday angles in this book use the sexagesimal English degrees system.
Main ideas
1. DEGREES MINUTES SECONDS: In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec. 2. OTHER SYSTEMS: Centesimal measure divides a right angle into 100 grades.
Why it matters
Write 40 deg 20 min, not a mix of grades. If a calculator is in radian mode, a 90 deg sine will look wrong. Sexagesimal means base 60, which is why minutes and seconds come in sixties.
How to answer in an exam
Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a decimal degree into minutes.
Explanation
Write 40 deg 20 min, not a mix of grades. If a calculator is in radian mode, a 90 deg sine will look wrong. Sexagesimal means base 60, which is why minutes and seconds come in sixties.
In simple words
Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a decimal degree into minutes.
Key points
- sexagesimal
- English degrees
- 1 deg = 60 min = 3600 sec
- Centesimal
- 1 deg = 60 min
- 1 deg = 3600 sec
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Sexagesimal Measure
Sticky Notes · Quick Revision
Core Idea
- Everyday angles in this book use the sexagesimal English degrees system.
Key Terms
- sexagesimal: Everyday angles in this book use the sexagesimal English degrees system.
- English degrees: Everyday angles in this book use the sexagesimal English degrees system.
Main Pattern
- 1. DEGREES MINUTES SECONDS: In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec.
- 2. OTHER SYSTEMS: Centesimal measure divides a right angle into 100 grades.
Worked Reminder
- 90 deg is a right angle
- 30 min is half of 1 deg
- 1 deg 30 min = 1.5 deg
Common Mistake
- Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a decimal degree into minutes.
Exam Tip
- State the rule for sexagesimal measure, show each algebraic step, and check the final answer against the question.
60-second revision
- Everyday angles in this book use the sexagesimal English degrees system.
- In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec.
- Centesimal measure divides a right angle into 100 grades.
- Write 40 deg 20 min, not a mix of grades.
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