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

Solution Of Rectilinear Figures, Find the number of square feet of pavement...

Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.

Draw a common graph f ( x ) = |x|, Graph f ( x ) = |x| Solution The...

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

Number theory, show that all primes except 2, are of the form 4n-1 or 4n+1...

show that all primes except 2, are of the form 4n-1 or 4n+1.

Twelve coworkers go out how many slices will each person get, Twelve cowork...

Twelve coworkers go out for lunch together and sequence three pizzas. Each pizza is cut within eight slices. If each person gets the similar number of slices, how many slices will

What is the widest piece of sheetrock, A door height is 6 feet and 6 inches...

A door height is 6 feet and 6 inches and 36 inches wide. What is the widest piece of sheetrock that will ?t through the door? Round to the nearest inch. a. 114 in b. 86 in

Prove that ac2 =ab2 + bc2+2bcxbd, If ABC is an obtuse angled triangle, obtu...

If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans:    AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A

Algebra function., problem to understand an problem; f(X-2)=X+3 / X-4

problem to understand an problem; f(X-2)=X+3 / X-4

Prove that ac2 = ap2 + 2(1+2)bp2, ABC is a right-angled isosceles triangle,...

ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans:    AC = √2AB (Sinc

how large a sample is necessary to have a standard error, If the populatio...

If the population standard deviation is o=8, how large a sample is necessary to have a standard error that is: a.  less than 4 points? b.  less than 2 points? c.  less than 1 poin

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