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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
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    - Calculus Preview

Radian, Degree Measure and the Unit Circle of Trigonometric Functions

Topic Review on "Title":


An angle consists of two rays, R1 and R2, with a common vertex.


Standard position of an angle:

An angle is said to be in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.


Co-terminal angles:

Two angles in standard position are said to be co-terminal if they have the same initial and terminal sides.


Arc length:

For a circle of radius , a central angle of  radius subtends and arc whose length is


 is measured in radians.

Area of a sector:

The area of the sector of a circle of radius formed by a central angle  radians is

 where the unit of angle  must be in radians.


Linear speed: The linear speed is defined as .

Angular speed:  The angular speed is defined as .

The domain of the sine function:

The domain of the sine function is the set of all real numbers.

The domain of the cosine function:

The domain of the cosine function is the set of all real numbers.


Periodic function:

A function is called periodic if there is a positive number such that, whenever  is in the domain of so is and . P is the period of


The Period of sine and cosine functions:

The period of sine and cosine functions is

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 covers angles and the relation of angles with respect to radians and trigonometric functions. The angle measure is represented in different ways as it is shown in the examples. The properties of angles are mentioned along with their use in trigonometry problems. 

Next the area of a sector is shown through the use of angles and the radius of a circle. Finally, the concept of a trigonometric function is discussed with the use of the unit circle. Calculation of the values of trigonometric functions of a quadrantal angle is shown with visual examples. The use of calculators to find values of trigonometric functions is important to the understanding of how you approximate trig functions.

Tutorial Features:

Specific Tutorial Features:
• Example problems with step by step solutions and accompanying diagrams to help illustrate the usage of angles in finding the values of trigonometric functions.

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:
        Definition of angles
        Standard position
Measure of angles
        Degrees and radians
Relation between degrees and radians
        Area of a sector
Circular motion
        Linear speed and angular speed
Trigonometric function
        Unit circle
Calculating the values of trigonometric functions using a calculator
Properties of the sine and cosine functions
	     Domain of the sine and cosine function
        Periodicity of sine and cosine function
        Example of sine and cosine function

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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