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Right Triangle Trigonometry and Trigonometric Functions of Any Angle

Topic Review on "Title":

Right triangle: A triangle in which one angle is a right angle

 Trigonometric functions on a circle with radius r:

For any angle  in standard position, let be the point on the terminal side of  that is also on the circle .

 ,, , , , and .

 The trigonometric functions of an acute angle:

If  is an acute angle of a right triangle, the six trigonometric functions of  are as follow:

, , , , , and .

 Complementary angles:

Two angles are called complementary if their sum equals to 90 degrees.

 Angle of elevation:

The acute angle measured from the horizontal to a line-of-sight observation of the object.

 Angle of depression:

The acute angle made by the line-of –sight observation of the object and the horizontal.

 The trigonometric functions of any angle:

Let  be an angle in standard position and let P(x,y) be a point, not the origin, on the terminal side that can be in any quadrant. If is the distance from the origin to the point P(x,y), then

, , , , , and

Trigonometric identities:

, , ,  and .

Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial describes right angle trigonometry in a variety of ways.  First, the trigonometric functions of acute angles are mentioned along with the complementary angle theorem. Solving right triangles is shown with the use of examples and trigonometric functions on a circle with radius r.

Next, applications of trigonometric functions are shown in the examples. It is important to use problem solving techniques when dealing with trigonometry application problems. Last, the use of right triangle is used to find the trigonometric functions of any angle. Evaluating the values of a trigonometric function is shown with the use of a calculator and graphical examples.

Tutorial Features:

Specific Tutorial Features:
• Graphic representation of right triangles to show the trigonometric functions.
• Example problems showing the different relations between x, y and r.
• Pneumonic memory device for remembering all the trigonometric functions with the respect to the sides of a right triangle.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

"Title" Topic List:
Right triangle The trigonometric functions on a circle with radius r Right angle trigonometry The trigonometric functions of an acute angle Complementary angles Co-functions Solving right triangles Applications of trigonometric functions Angle of elevation Angle of depression Trigonometric functions of any angle Trigonometric functions of a real number t Identities Evaluating the values of a trigonometric function The sign of the trigonometric functions Reference angles

See all 24 lessons in Pre-Calculus, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Pre-Calculus Visually in 24 Hours

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