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Trigonometric Ratios




 
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More Lessons for Geometry

More Lessons for High School Geometry

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A series of free, online High School Geometry Video Lessons and solutions.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • how to find the sine of an angle in a right triangle
  • how to find the cosine of an angle in a right triangle
  • how to find the tangent of an angle in a right triangle
  • how to use inverse trigonometric functions to find an angle with a given trigonometric value


Trigonometric Ratios: Sine

Right triangles have ratios to represent the angles formed by the hypotenuse and its legs. Sine ratios, along with cosine and tangent ratios, are ratios of the lengths of two sides of the triangle. Sine ratios in particular are the ratios of the length of the side opposite the angle they represent over the hypotenuse. Sine ratios are useful in trigonometry when dealing with triangles and circles.
How to define the sine ratio and identify the sine of an angle in a right triangle.
A word problem involving the trigonometric ratio of sine to calculate the height of a pole



Trigonometric Ratios: Cosine

Right triangles have ratios that are used to represent their base angles. Cosine ratios, along with sine and tangent ratios, are ratios of two different sides of a right triangle.Cosine ratios are specifically the ratio of the side adjacent to the represented base angle over the hypotenuse. In order to find the measure of the angle, we must understand inverse trigonometric functions.
This video illustrates how to use the Cosine formula (the CAH Formula)
This video explains the cosine ratio and gives an example.
Apply the Sine and Cosine Ratios


 

Trigonometric Ratios: Tangent

Right triangles have ratios that are used to represent their base angles. Tangent ratios, along with cosine and sine ratios, are ratios of two different sides of a right triangle. Tangent ratios are the ratio of the side opposite to the side adjacent the angle they represent. In order to find the measure of the angle itself, one must understand inverse trigonometric functions.
This video illustrates how to use the Tangent formula (the TOA Formula)
Solving Problems with the Tangent Ratio


Inverse Trigonometric Functions

Once we understand the trigonometric functions sine, cosine, and tangent, we are ready to learn how to use inverse trigonometric functions to find the measure of the angle the function represents. Inverse trigonometric functions, found on any standard scientific or graphing calculator, are a vital part of trigonometry and will be encountered often in Calculus.
This video shows how to use inverse trigonometric functions to find an angle with a given trigonometric value and how to use inverse trigonometric functions to solve a right triangle.
Inverse trig functions are used to find missing angles rather than missing sides. This video explains how to use inverse trig to find a missing angle.


 
Find missing Angles - Using Inverse Sine, Cosine, Tangent


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