November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Right triangle and trigonometric functions.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions, right triangle and their relationship. You'll learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The three primary trigonometry functions are: sin*x*, cos *x*, tan *x*. The input value usually represents an angle. The length of three sides of a right triangle, are simply termed as the ‘opposite’. ‘adjacent’ and ‘hypotenuse’. The values for the trigonometric functions are defined as the value that you get when divided one side by the other side i.e. ratio of one side to the other. E.g. sin *x* = opposite / hypotenuse.

Further you’ll explore, how you can use the ratios of side-length of right triangles to determine the measures of sides and angles. We’ll apply the Pythagorean Theorem, concept of ratio and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. E.g. In a right triangle*ABC*, with sides *a*, *b* and *c*, you need to remember:
*a* = 10 and *b* = 24, then

*c*^{2} = *a*^{2} + *b*^{2} = 10^{2} + 24^{2} = 100 + 576 = 676.

The square root of 676 is 26, so*c* = 26.

This mini-lesson introduces and walks you through the basic concepts of the trigonometric functions, right triangle and their relationship. You'll learn it with the help of some examples, practice questions with solution, using video and explanation in own handwriting by the instructor that brings in an element of real-class room experience.

The three primary trigonometry functions are: sin

Further you’ll explore, how you can use the ratios of side-length of right triangles to determine the measures of sides and angles. We’ll apply the Pythagorean Theorem, concept of ratio and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. E.g. In a right triangle

- Pythagorean theorem:
*a*^{2}+*b*^{2}=*c*^{2} - Sines: sin
*A*=*a*/*c*, sin*B*=*b*/*c* - Cosines: cos
*A*=*b*/*c*, cos*B*=*a*/*c* - Tangents: tan
*A*=*a*/*b*, tan*B*=*b*/*a*

The square root of 676 is 26, so

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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