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Math Study Lounge
These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.
    - Getting Started with Algebra
    - Geometry Basics
    - How to Solve Math Problems
    - Trigonometry Quick Review
    - Statistics At-A-Glance
    - Calculus Preview

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 mentions right triangle and its formulation. The complementary angle theorem is mentioned with the use of the trigonometric functions of acute angles. The use of a circle with radius r is needed to solve right triangles.

Right triangle relations and properties are used to find the trigonometric values of any angle. Examples are shown to emphasize the importance of right triangle trigonometry and its relation with the trigonometric functions of any angle.

Tutorial Features:

Specific Tutorial Features:
• The trigonometric functions are shown with the use of the graphical representation of right triangles.
• Example problems showing the different trigonometric functions that are found with the use of the 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-function angles and their properties
Solving right triangles
Applications of trigonometric functions
Angle of elevation examples
Angle of depression examples
Trigonometric functions of any angle
Trigonometric functions of a real number t
Trigonometric identities
Evaluating the values of a trigonometric function
The sign of the trigonometric functions
Reference angles

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

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