Unit Circle and the Trigonometric Functions sin(x), cos(x) and tan(x)


Using the unit circle, you will be able to explore and gain deep understanding of some of the properties, such as domain, range, asymptotes (if any) of the trigonometric functions.








Web www.analyzemath.com

Online Geometry Calculators and Solvers

Precalculus Tutorials

Graphing Functions

Calculus Tutorials and Problems

Calculus Questions with Answers

Trigonometry Tutorials and Problems for Self Tests

Geometry Tutorials and Problems

Math problems

solving Equation and Inequalities

Graphs of Functions, Equations, and Algebra (applest)

Online Math Calculators and Solvers

Elementary statistics and Probability Tutorials

Math Software (applets)

Applications of Mathematics in Physics and Engineering

Antennas

Free Calculus Worksheets to Download

free math worksheets to download

Free trigonometry worksheets to download

Free Geometry Worksheest to Download

Free graph paper

The relationships between the graphs (in rectangular coordinates) of sin(x), cos(x) and tan(x) and the coordinates of a point on a unit circle are explored using an applet.

Definitions

1- Let x be a real number and P(x) a point on a unit circle such that the angle in standard position whose terminal side is segment OP is equal to x radians.(O is the origin of the system of axis used).

2- We define sin(x) as the y-coordinate of point P(x) on the unit circle.

3- We define cos(x) as the x-coordinate of a point P(x) on the unit circle.

4- We define tan(x) as the ratio of the y-coordinate and x-coordinate of point P(x) on a unit circle.

Interactive Tutorial Using Applets

Two possibilities to explore trigonometric function using the unit circle.

1) Using a Unit Circle HTML5 Applet
or
A java applet below
Your browser is completely ignoring the <APPLET> tag!

  1. Is there a point P(x) that cannot have any values for its x or y-coordinates? The x and y-coordinates are cos(x) and sin(x), what is the domain of sin(x), what is the domain of cos(x)?
    answer

  2. Explore the x-intercepts, the maximums and minimums (if any) of the graphs of sin(x) and cos(x) using the unit circle.
    answer

  3. Using the unit circle, do you think that any of the coordinates of a point on the circle can be larger than 1 or smaller than -1. Why do you think that sin(x) and cos(x) cannot be larger than 1 or smaller than -1?
    answer

  4. Explore the periodicity of sin(x), cos(x) and tan(x).
    answer

  5. tan(x)is the ratio y-coordinate / x-coordinate and whenever the x-coordinate of point P(x) is equal to zero, we cannot define tan(x).Find these points for x between zero and 2Pi. What is the domain of tan(x)?
    answer

  6. At these same points where tan(x)is undefined, the graph of tan(x) on the right shows an asymptotic behavior, Explain. What do you think is the range of tan(x)? Find all x-intercepts of tan(x) between 0 and 2Pi (inclusive). Explain their positions on the x-axis.
    answer

More references on unit circle and trigonometric functions.
http://analyzemath.com/unitcircle/unit_circle_video_1.html






Interactive HTML5 Math Web Apps for Mobile LearningNew !
Free Online Graph Plotter for All Devices
Home Page -- HTML5 Math Applets for Mobile Learning -- Math Formulas for Mobile Learning -- Algebra Questions -- Math Worksheets -- Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests -- GRE practice -- GMAT practice Precalculus Tutorials -- Precalculus Questions and Problems -- Precalculus Applets -- Equations, Systems and Inequalities -- Online Calculators -- Graphing -- Trigonometry -- Trigonometry Worsheets -- Geometry Tutorials -- Geometry Calculators -- Geometry Worksheets -- Calculus Tutorials -- Calculus Questions -- Calculus Worksheets -- Applied Math -- Antennas -- Math Software -- Elementary Statistics High School Math -- Middle School Math -- Primary Math
Math Videos From Analyzemath
Author - e-mail


Updated: 2 April 2013

Copyright © 2003 - 2014 - All rights reserved