OML Search

Trigonometric Functions / Trigonometric Ratios




 
In these lessons, we will look at the three basic trigonometric functions (or trigonometric ratios), Sine, Cosine and Tangent and how they can be used to find missing sides and missing angles. We will also learn how to solve multi-step SOHCAHTOA problems.

Related Topics:
More Lessons on Trigonometry

Trigonometric Functions: Sine of an Angle

We first consider the sine function.

The sine of an angle is the ratio of the opposite side to the hypotenuse side.

Sine is usually abbreviated as sin. Sine θ can be written as sin θ .

You may use want to use some mnemonics to help you remember the trigonometric functions. One common mnemonic is to remember the Indian Chief SOH-CAH-TOA.

Example:

Calculate the value of sin θ in the following triangle.


Solution:




Using the Sine Formula (the SOH formula)
This is part 1 of a video that teaches how to use the SOH formula in high school Trigonometry.
This is part 2 of a video that teaches how to use the SOH formula in high school Trigonometry.


 

Trigonometric Functions: Cosine of an Angle

Next, we consider the cosine function.

The cosine of an angle is the ratio of the adjacent side and hypotenuse side.

Cosine is usually abbreviated as cos. Cosine θ can be written as cos θ .

Example:

Calculate the value of cos θ in the following triangle.


Solution:

Using the Cosine Formula (the CAH formula)
This video illustrates how to use the Cosine formula (the CAH Formula) in high school trigonometry courses.


Trigonometric Functions: Tangent of an Angle

Next, we first consider the tangent function.

The tangent of an angle is the ratio of the opposite side and adjacent side.

Tangent is usually abbreviated as tan. Tangent θ can be written as tan θ.


Example:

Calculate the value of tan θ in the following triangle.


Solution:


Using the Tangent Formula (the TOA formula)
This video illustrates how to use the Tangent formula (the TOA Formula) in high school trigonometry.


 

Solving problems using SOHCAHTOA

Have a look at the following video for more examples of the trigonometric functions.
A review of basic trigonometry: Sine, Cosine & Tangent including how to use the ratios to find missing sides and missing angles on right triangles.
Find the trigonometric ratios for the right triangle.


Multiple-Step SOH CAH TOA Problems - Example 1
This video illustrates how to use the SOH, CAH and TOA formulas from basic trigonometry to solve problems that involve the use of more than one formula.
Example: Two ladders are leaning against a building as shown. What is the angle below the shorter angle?
Multiple-Step SOH CAH TOA Problems - Example 2
Example: A warbler and a cardinal are perched at the top of two trees. Given the angle of inclination between the apple and the birds, which bird is closer to the apple and by how much?


 
Multiple-Step SOH CAH TOA Problems - Example 3
How long is side UX?
Multiple-Step SOH CAH TOA Problems - Example 4
What is the measure of the angle?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget which allows your to practice solving Algebra, Trigonometry, Calculus and other math topics.


You can use the Mathway widget below to practice Trigonometry or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines