Unit circle, Mathematics

Assignment Help:

Unit circle: The unit circle is one of the most valuable tools to come out in trig.  Unluckily, most people don't study it as well.

Below is the unit circle with just the first quadrant filled in is represented. The process the unit circle works is to draw a line from the center of the circle outside corresponding to a given angle. Then notify at the coordinates of the point where the line & the circle intersect. The first coordinate is the cosine of that angle & the second coordinate is the sine of that angle. We've put some of the basic angles along with the coordinates of their intersections on the unit circle.  Hence, from the unit circle below we can illustrates that cos (? /6 ) = √3 /2 and sin (?/6)= 1/2 .

1143_unit circle.png

Keep in mind how the signs of angles work.  If you rotate into a counter clockwise direction the angle is +ve and if you rotate into a clockwise direction the angle is negative.

Remember as well that one complete revolution is 2 ? , thus the positive x-axis can correspond to either an angle of 0 or 2 ? (or 4 ? , or 6 ? , or -2 ? , or -4 ? , etc. based on the direction of rotation). Similarly, the angle ? /6 given angles: (to pick an angle totally at random) can also be any of the

? /6  +2 ? = 13 ?/6  (start at ? /6  then rotate once around counter clockwise)

? /6  + 4 ? = 25 ?/6  (start at ?/6  then rotate around twice counter clockwise)

? /6  -2 ?=11 ?/6 (start at ?/6      then rotate once around clockwise)

? /6  - 4 ? = 23 ?/6   (start at ?/6 then rotate around twice clockwise)

etc.

Actually ?/6 can be any of the given angles  ?/6 + 2 ? n , n = 0, ±1, ± 2, ±  3,.. In this case n refer to the number of complete revolutions you make around the unit circle begining at 6  .  Positive values of n correspond to counter clockwise rotations & -ve values of n correspond to clockwise rotations.

If you know the first quadrant then you can easily get all the other quadrants from the first along with a small application of geometry.


Related Discussions:- Unit circle

Definition of relation, Definition of Relation A relation is a set of o...

Definition of Relation A relation is a set of ordered pairs. It seems like an odd definition however we'll require it for the definition of a function though, before actuall

Operations research, scope of operation research and its limitations

scope of operation research and its limitations

Area related to circles, railway tunnel of radius 3.5 m and angle aob =90 f...

railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

Example of 3-d coordinate system, Example of 3-D Coordinate System Exam...

Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 .   Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co

Fraction, Ask question #Minimum 100 words accepted

Ask question #Minimum 100 words accepted

Example to understand means to count, Place ten pebbles (or any other such ...

Place ten pebbles (or any other such objects) in front of a child who can recite number names upto ten in the correct sequence. Ask him/her to count them aloud while touching the p

Illustrate pythagorean theorem, Q. Illustrate Pythagorean Theorem? Ans...

Q. Illustrate Pythagorean Theorem? Ans. You have definitely seen the Pythagorean Theorem before, so a 2 + b 2 = c 2 should look familiar to you. The Pythagorean Theor

Evaluate the area and perimeter of a square, Evaluate the area and perimete...

Evaluate the area and perimeter of a square: Example: Calculate the area and perimeter of a square with a = 5´.  Be sure to include units in your answer. Solution:

School mathematics, I am interested in school mathematics online assignment...

I am interested in school mathematics online assignments , homework help, projects etc. I have good knowledge of mathematics and experience of 15+ years teaching mathematics in cen

Algebra, how do i sole linear epuation

how do i sole linear epuation

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd