Question

how do i find the sin 11pi/2 without using a calculator?

Answer 1

thats a fix value. sin (pi/2) = 1

Answer 2

\[\frac{11 \pi}{2}\] on the unit circle and look at the second coordinate

Answer 3

i get it that it = 990 degrees but how do i get it in point form

Answer 4

\[\sin(\frac{11\pi}{2})=\sin(\frac{10\pi}{2}+\frac{\pi}{2})\]

Answer 5

if you like you can
a) count
b) subtract of 2pi repeatedly until you get a number between 0 and 2 pi

Answer 6

draw a circle; and place an angle that sweeps out 11pi/2 ; and measure how far its terminal end point is from the x axis :)

Answer 7

Oh.. It's 11pi/2. Sorry i misread the question.

(11/2)pi = 5pi + pi/2
5pi = two and a half turn around the trignometric circle. if you sum more pi/2 then you're in (3/2)pi = -1

Answer 8

\[\sin(5\pi+\frac{\pi}{2})\]
this is as far as i can go
my teacher always said to chance it

Answer 9

in any case the answer is NOT 1

Answer 10

lets do it the simple donkey way. make life easy

Answer 11

\[\sin x = \sum_{n=1}^{\infty} (-1/(2n+1)!)*x^{2n+1}\]

Answer 12

\[\frac{11}{2}=5\tfrac{1}{2}\]
subtract 4 get
\[1\tfrac{1}{2}=\frac{3}{2}\]

Answer 13

sin(5pi)cos(pi/2)+sin(pi/2)cos(5pi)
0*0+1*(-1)
-1

Answer 14

so just locate
\[]\frac{3\pi}{2}\] on the unit circle. you will see that the second coordinate is -1 (not 1) and that is your answer

Answer 15

i just plugged it into the formula i seen online

Answer 16

this is all way way way too much work. give the guy (gal) a break

Answer 17

thanks everyone i get it now

Answer 18

really this is very easy and straight forward

Answer 19

wait satelite why did you subtract 4?

Answer 20

no formula, not infinite sum lordamercy. just look at
\[\frac{3\pi}{2}\] and see where you are. finito

Answer 21

11pi/2=10pi/2+1pi/2 right?
5pi+pi/2

Answer 22

Draw a Unit Circle, label, pi, pi/2, 3pi/2, and 2pi....Then start with pi/2 and keep going around the unit circle until you get to 11pi/2. one pi/2....2pi/2...3pi/2....etc.

Answer 23

@chelsea i subtract 4 because i am working with
\[\frac{11}{2}\] instead of
\[\frac{11\pi}{2}\] sometimes the pi throws you off

Answer 24

so what i was really doing was subtracting off
\[2\pi\] as many times as i could to end up between 0 and 2 pi

Answer 25

My method requires no adding, subtracting, multiply, dividing or any of that complicated stuff, just the ability to count and go around a unit circle.

Answer 26

for example if i see
\[\frac{25\pi}{2}\] i think to myself
\[\frac{25}{2}=12\tfrac{1}{2}\] and 2 goes in to 12 evenly so this is the same as
\[\frac{1}{2}\] i.e.
\[\frac{25\pi}{2}\] is coterminal with
\[\frac{\pi}{2}\] and i look there.

Answer 27

@hero of course you are right and i frequently count as well. but suppose you had
\[\frac{25\pi}{2}\] are you really going to count?

Answer 28

counting to eleven is ok but i have no desire to count to twenty five going around and around and around

Answer 29

i mean i have done exactly what you wrote many times.
one pi over two
two pi over two
three pi over two
four pi over two etc, but at some point you do not want to do this

Answer 30

dude... if it's even than its an entire turn around the circle. which means you're in position 0 again. or 2pi if you want.
if it's odd than you're in half turn of only pi

Answer 31

oooooh i get it so just simplify and it will be coterminal ?

Answer 32

right exactly. you want to end up between 0 and 2 pi

Answer 33

You can use other methods to get there quicker.....12pi/2 = 6 pi.....24/2 = 12pi which are all multiples of 2pi, you just count one more, and you have the eqivalent of 25pi/2 which is pi/2

Answer 34

by subtracting off two pi as many times as you can. which is the same as dividing by 2 and taking the remainder

Answer 35

which is what hero is saying if i understand him correctly

Answer 36

3pi/2 around the circle

then pi/2+3pi/2 to end up at same spot

pi/2+(pi/2+3pi/2) to end again at same point

;;;;;


8*pi/2+3pi/2

Answer 37

No....I'm counting....

Answer 38

Either way, the unit circle method is simpler

Answer 39

actually you divided 12 by 2 just as i did. it is the same

Answer 40

Ah, there's a subtle difference

Answer 41

you can call it counting but you wrote
\[\frac{12\pi}{2}=6\pi\] and i said 2 goes in to twelve evenly, this is the same

Answer 42

believe me i am not trying to say that you are wrong, just that we are really doing the same thing

Answer 43

The difference is, I don't keep subtracting 2pi, I only started with 12pi/2 for explanation purposes....I could have simply started with 24pi/2 = 12pi which is a multiple of 2pi

Answer 44

and then simple count 1 more and I have pi/2

Answer 45

hey satelite what did u do with that extra pi/2 left over again?

Answer 46

yes and i maintain that they are the same procedure. saying the remainder when i divide 25 by 2 is 1 is the same as saying i subtract 2 12 times leaving 1. of course i am not actually subtracting 2 12 times, i am dividing

Answer 47

My method works for those who are not adept and subtracting and dividing...that's the difference

Answer 48

@chelsea you locate
\[\frac{\pi}{2}\] on the unit circle, and look at the second coordinate of you want sine and first if you want cosine. and excellent cheat sheet is here
http://tutorial.math.lamar.edu/cheat_table.aspx

Answer 49

look at the trig cheat sheet. it has a nice unit circle on it

Answer 50

thanks !

Answer 51

unit circle on last page it has it all mapped out for you

Answer 52

You don't add, you don't subtract, you don't multiply, you don't divide. You just simply "count". It's the same with those sensor activated toilet flushers. You don't touch the lever, you just simply dump and go

Answer 53

@hero what is coterminal with
\[\frac{127\pi}{4}\] and how would you find it without dividing?

Answer 54

ooh one last thing so what i locate is the remainder for all other problems>?

Answer 55

i do like the flush analogy

Answer 56

You got me on that one....I was referring to stuff under 30pi/2 or 30pi/4....anything like that and you'll at least have to divide

Answer 57

find the nearest muliple of 4

Answer 58

Which is 31pi, then you're left with 3pi/4