How to Learn Trigonometry
Define the parts of a triangle., Learn to make unit circle., Know the trigonometric functions., Conceptualize relationships.
Step-by-Step Guide
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Step 1: Define the parts of a triangle.
At it’s core, trigonometry is the study of relationships present in triangles.
A triangle has three sides and three angles.
By definition, the sum of angles for any triangle is 180 degrees.
You should familiarize yourself with triangles and triangle terminology to succeed in trigonometry.
Some common triangle terms are:
Hypotenuse ― The longest side of a triangle.
Obtuse ― An angle that is greater than 90 degrees.
Acute ― An angle less than 90 degrees. -
Step 2: Learn to make unit circle.
A unit circle allows you to scale any triangle so that the hypotenuse is equal to one.
This is helpful because it relates trigonometric functions, like sine and cosine to percents.
Once you understand the unit circle, you can use trigonometric values for a given angle to answer questions about triangles with those angles.Example 1:
The sine of 30 degrees is
0.50.
This means that the side opposite a 30 degree angle is exactly one half the length of the hypotenuse.
Example 2:
This relationship could be used to find the length of the hypotenuse in a triangle that has a 30 degree angle with the side opposite that angle measuring 7 inches.
The hypotenuse would be equal to 14 inches. , There are six functions that are central to understanding trigonometry.
Together, they define the relationships within a triangle, and allow you to understand the unique properties of any triangle.
These six functions are:
Sine (Sin) Cosine (Cos) Tangent (Tan) Secant (Sec) Cosecant (Csc) Cotangent (Cot) , One of the most important things to understand about trigonometry is that all of the functions are interrelated.
While values for Sine, Cosine, Tangent, etc. all have their own uses, they are most useful because of the relationships that exist between them.
The unit circle scales these relationships down so that they are easily understood.
Once you understand the unit circle, you can use the relationships it describes to model other problems. -
Step 3: Know the trigonometric functions.
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Step 4: Conceptualize relationships.
Detailed Guide
At it’s core, trigonometry is the study of relationships present in triangles.
A triangle has three sides and three angles.
By definition, the sum of angles for any triangle is 180 degrees.
You should familiarize yourself with triangles and triangle terminology to succeed in trigonometry.
Some common triangle terms are:
Hypotenuse ― The longest side of a triangle.
Obtuse ― An angle that is greater than 90 degrees.
Acute ― An angle less than 90 degrees.
A unit circle allows you to scale any triangle so that the hypotenuse is equal to one.
This is helpful because it relates trigonometric functions, like sine and cosine to percents.
Once you understand the unit circle, you can use trigonometric values for a given angle to answer questions about triangles with those angles.Example 1:
The sine of 30 degrees is
0.50.
This means that the side opposite a 30 degree angle is exactly one half the length of the hypotenuse.
Example 2:
This relationship could be used to find the length of the hypotenuse in a triangle that has a 30 degree angle with the side opposite that angle measuring 7 inches.
The hypotenuse would be equal to 14 inches. , There are six functions that are central to understanding trigonometry.
Together, they define the relationships within a triangle, and allow you to understand the unique properties of any triangle.
These six functions are:
Sine (Sin) Cosine (Cos) Tangent (Tan) Secant (Sec) Cosecant (Csc) Cotangent (Cot) , One of the most important things to understand about trigonometry is that all of the functions are interrelated.
While values for Sine, Cosine, Tangent, etc. all have their own uses, they are most useful because of the relationships that exist between them.
The unit circle scales these relationships down so that they are easily understood.
Once you understand the unit circle, you can use the relationships it describes to model other problems.
About the Author
Justin Gonzalez
A passionate writer with expertise in creative arts topics. Loves sharing practical knowledge.
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