Evaluate following unit circle, Mathematics

Assignment Help:

Evaluate following sin 2 ?/3   and sin (-2 ?/3)

Solution: The first evaluation in this part uses the angle 2 ?/3.  It is not on our unit circle above, though notice that  2 ?/3= ? - ?/3 .  thus 2 ?/3 is found through rotating up from the -ve  x-axis.

It means that the line for 2 ?/3 will be a mirror image of the line for ?/3 only within the second quadrant. The coordinates for 2 ?/3   will be the coordinates for ?/3 except the x coordinate will be negative.

Similarly for - 2 ?/3 we can notice that - 2 ?/3  = - ?+  ?/3   , hence this angle can be found by rotating down ?/3   from the -ve x-axis. It means that the line for ?/3  will be a mirror image of- 2 ?/3 the line for ?/3  only in the third quadrant and the coordinates will be the same as the coordinates for ?/3  except both will be negative.

Both of these angles along with their coordinates are illustrated on the following unit circle.

2251_unit circle point.png

From this unit circle we can see that sin ( 2 ?/3  ) =√3/2 and sin ( -2 ?/3  )=√3/2

It leads to a nice fact regarding the sine function. The sine function is known an odd function and hence for any angle we have

                                          sin ( - θ ) = - sin (θ )


Related Discussions:- Evaluate following unit circle

Math, is this free for LIFE that means forever never ever going to pay

is this free for LIFE that means forever never ever going to pay

Developing pre-number concepts, DEVELOPING PRE-NUMBER CONCEPTS :  Previous...

DEVELOPING PRE-NUMBER CONCEPTS :  Previously you have read how children acquire concepts. You know that, for children to grasp a concept, they must be given several opportunities

Simplification, how do we answer questions with fraction mixed. what are th...

how do we answer questions with fraction mixed. what are the easier ways to do it

Complex, find all the 8th roots of (19+7i)

find all the 8th roots of (19+7i)

Exponents., the (cube square root of 2)^1/2)^3

the (cube square root of 2)^1/2)^3

How many inches is the smaller dimension of the decreased, A photographer d...

A photographer decides to decrease a picture she took in sequence to fit it within a certain frame. She requires the picture to be one-third of the area of the original. If the ori

Geometry of convex sets, (a) Given a norm jj jj on Rn, express the closed b...

(a) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by

Determine the probability of given question, Q. Assume a birthday is equall...

Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:

DETERMINANT, IF 7 AND 2 ARE TWO ROOTS OF THE EQUATION |X 3 7 2 X 2 7 6 X...

IF 7 AND 2 ARE TWO ROOTS OF THE EQUATION |X 3 7 2 X 2 7 6 X |=0 THEN FIND THE THIRD ROOT IS

Multiplication of two matrices, Need assignment help, Explain Multiplicatio...

Need assignment help, Explain Multiplication of two Matrices.

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