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

Ellipse, alpha and beta are concentric angles of two points A and B on the ...

alpha and beta are concentric angles of two points A and B on the ellipse.

Find the polynomial g(x), On dividing the polynomial 4x 4 - 5x 3 - 39x 2 ...

On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +

If a sequence is bounded and monotonic then it is convergent, Theorem ...

Theorem If {a n } is bounded and monotonic then { a n } is convergent.  Be cautious to not misuse this theorem.  It does not state that if a sequence is not bounded and/or

Properties of dot product - proof, Properties of Dot Product - proof P...

Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof.  Let us start with v → = (v1 , v2 ,.... , vn) a

E is irrational, If e were rational, then e = n/m for some positive integer...

If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v

Linear functions, Linear functions are of the form: y = a 0 ...

Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a

Relative maximum point, Relative maximum point The above graph of the ...

Relative maximum point The above graph of the function slopes upwards to the right between points C and A and thus has a positive slope among these two points. The function ha

Trigonometry, I am really stuck on this topic and other topics its extremel...

I am really stuck on this topic and other topics its extremely difficult and I dont know what to do Im stressing out help me please.

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