Context:
1) Introduction
2) Things you need to know to understand trigonometry
Geometry
Angles
Unit Circle
3) Reason to study trigonometry
4) Degree and Radian
Degree
Why 360 in a circle or revolution
Radian
5) Trigonometric ratios
6) Trigonometric Functions
7) Coordinate system with quadrant topic
x and y values according to quadrant
Values of Trigonometric functions in different quadrants
8) Arc Length
9) Questions
10) Summary
Trigonometry is a field of mathematics that examines the connections between the
sides and angles of triangles. The word trigonometry comes from the Latin derivative of
Greek words for the triangle (trigonon) and measure (metron), wait this is the way
everyone teaches, a typical way but my way is different. I will make sure that you will
remember the things you will learn in these notes, I added some things that will help you
remember things without memorizing them in a typical way.
These notes are designed to break down complex topics into simple, understandable
parts to ensure you never feel left behind or overwhelmed. I've included plenty of
practice exercises to help you apply what you’ve learned. The notes are structured in a
clear, organized manner to make it easy for you to follow along and review later. I aim to
accommodate different learning styles, so whether you prefer reading, visual aids, or
hands-on practice, there’s something here for you.
Additionally, I am always available for extra help if you have any questions or need
further clarification, feel free to contact me on my Instagram (Almas_urfellowstudent).
,Things you need to know to understand
trigonometry:
First of all, I want to talk about things you must know to grasp the concept of
trigonometry.
1) Geometry
Right Triangle:
What it is: A triangle with one angle exactly 90 degrees.
Properties: The side opposite the right angle is the hypotenuse (the longest
side).
Pythagorean Theorem:
What it is: A formula to find the length of a side in a right triangle.
Formula: a2 + b2 = c2, where c is the hypotenuse, and a and b are the other two
sides.
Example:
Given: a = 3, b = 4
, Solution: 32 + 42 = c2
Calculation: 9 + 16 = c2 ⇒ 25 = c2 ⇒ c = 5
2) Angles
Measuring Angles:
Degrees: A unit for measuring angles. A full circle is 360 degrees.
Example: A right angle is 90 degrees.
Types of Angles:
Acute Angle: Less than 90 degrees.
Right Angle: Exactly 90 degrees.
Obtuse Angle: Greater than 90 degrees but less than 180 degrees.
Straight Angle: Exactly 180 degrees.
3) Unit Circle Basics
Unit Circle:
Definition: A circle with a radius of 1 centered at the origin (0,0) on a coordinate
plane.
Reason to Study Trigonometry:
At this point you may be wondering why we even have to learn this; the first reason is of
course it will be in your exam and the second thing is trigonometric functions are used
in obtaining unknown angles and distances from known or measured angles in
geometric figures to find height and distance.
Degree and Radian:
Degree:
1) Introduction
2) Things you need to know to understand trigonometry
Geometry
Angles
Unit Circle
3) Reason to study trigonometry
4) Degree and Radian
Degree
Why 360 in a circle or revolution
Radian
5) Trigonometric ratios
6) Trigonometric Functions
7) Coordinate system with quadrant topic
x and y values according to quadrant
Values of Trigonometric functions in different quadrants
8) Arc Length
9) Questions
10) Summary
Trigonometry is a field of mathematics that examines the connections between the
sides and angles of triangles. The word trigonometry comes from the Latin derivative of
Greek words for the triangle (trigonon) and measure (metron), wait this is the way
everyone teaches, a typical way but my way is different. I will make sure that you will
remember the things you will learn in these notes, I added some things that will help you
remember things without memorizing them in a typical way.
These notes are designed to break down complex topics into simple, understandable
parts to ensure you never feel left behind or overwhelmed. I've included plenty of
practice exercises to help you apply what you’ve learned. The notes are structured in a
clear, organized manner to make it easy for you to follow along and review later. I aim to
accommodate different learning styles, so whether you prefer reading, visual aids, or
hands-on practice, there’s something here for you.
Additionally, I am always available for extra help if you have any questions or need
further clarification, feel free to contact me on my Instagram (Almas_urfellowstudent).
,Things you need to know to understand
trigonometry:
First of all, I want to talk about things you must know to grasp the concept of
trigonometry.
1) Geometry
Right Triangle:
What it is: A triangle with one angle exactly 90 degrees.
Properties: The side opposite the right angle is the hypotenuse (the longest
side).
Pythagorean Theorem:
What it is: A formula to find the length of a side in a right triangle.
Formula: a2 + b2 = c2, where c is the hypotenuse, and a and b are the other two
sides.
Example:
Given: a = 3, b = 4
, Solution: 32 + 42 = c2
Calculation: 9 + 16 = c2 ⇒ 25 = c2 ⇒ c = 5
2) Angles
Measuring Angles:
Degrees: A unit for measuring angles. A full circle is 360 degrees.
Example: A right angle is 90 degrees.
Types of Angles:
Acute Angle: Less than 90 degrees.
Right Angle: Exactly 90 degrees.
Obtuse Angle: Greater than 90 degrees but less than 180 degrees.
Straight Angle: Exactly 180 degrees.
3) Unit Circle Basics
Unit Circle:
Definition: A circle with a radius of 1 centered at the origin (0,0) on a coordinate
plane.
Reason to Study Trigonometry:
At this point you may be wondering why we even have to learn this; the first reason is of
course it will be in your exam and the second thing is trigonometric functions are used
in obtaining unknown angles and distances from known or measured angles in
geometric figures to find height and distance.
Degree and Radian:
Degree:
