Question

what is sin 11pi/2 with working? and without using calcu..

Answer 1

with working?

Answer 2

pi = 180, substitute, then evaluate, then reduce

Answer 3

showing the proper solution

Answer 4

sin(pi/2) is 1 from unit circle. 11pi/2 should be the same except you must find the quadrant so you know the sign

Answer 5

sin 11pi/2 = sin pi/2 = 1

Answer 6

it's -1 cause it's not at pi/2 it's actually at 3pi/2

Answer 7

Moldy84 has the right answer and explanation.

Answer 8

sorry - u r right its at 3pi/2

Answer 9

I don't see anything wrong with my approach

Answer 10

the trigonometric function value also depends on the quadrant in which the angle lies.

Answer 11

yea, i just dont know how to get 3pi/2...

Answer 12

spiko, so 11pi/2 is pi/2 multiplied by 11 right?

Answer 13

that can put it at 90 degrees or 270 depending on how many times it went halfway around the unit circle

Answer 14

somtimes it lands at the pi/2 position. sometimes it lands at 3pi/2.

Answer 15

if it lands at the bottom then it's neg, if top then pos

Answer 16

Or you can think of it this way: pi/2 = 90 degrees, 1 full circle is 360 degree = 4 pi/2; then 8 pi/2 is 2 full circles; then you add 3 pi/2 to get to 11 pi/2

Answer 17

spiko, how come you didn't like my approach?

Answer 18

heromiles i butt hurt

Answer 19

moldy, im supposed to use this method.
example:
cos (-31pi/6) = - 30pi/6 - pi/6
= - 5pi - pi/6
= - √3/2
but i dont know how to apply it to that qn i asked

Answer 20

oh you are using reference angles

Answer 21

ok then. so 11pi/2 = 10pi/2 = pi/2
= 5pi-pi/2

Answer 22

sorry + not - on that arithmetic

Answer 23

sin(5pi) should always be zero then pi/2 but that doesn't really help us cause it's positive. it's been a long time since i've done this. forgive me. i always just think of the unit circle like i was explaining:\

Answer 24

sin (11pi/2) = 12pi/2 - pi/2
= 6pi - pi/2
= 5pi/2
sin 5pi/2 = -1.506

Answer 25

i'm pretty rusty at these too - is that the correct answer?

Answer 26

sorry sin 5pi/2 = 1

Answer 27

thanks guys...i do know how to get the ans from the unit circle but im supposed to just calculate it using the radians & coordinates of (x,y) & without the use of calcu...jimmy supposed to get 3pi/2 = -1...just really duno the correct way of doin it =/

Answer 28

Here's the way I did it:

sin(11pi/2) = sin(11*180/2) = sin (11*90) = sin(990) = sin (990 - 720) =
sin (270) = sin (3pi/2) = -1

Answer 29

jimmy you got it right i think

Answer 30

Jimmy didn't get it right...The answer is -1, not 1

Answer 31

yeah he's right

Answer 32

yep - good thinking hero - no moldy sin 5pi/2 gives 1 while sin 11pi/2 = -1

Answer 33

6pi = 0 then we take sin of -pi/2 = -1

Answer 34

sin(6pi)=0 not sure if we can split it like that. but then you ave the angle -pi/2 left and take the sin of that and you get -1

Answer 35

heromiles got the right answer

Answer 36

The way I did it is the easiest way to do it IMO

Answer 37

heromiles way works too. you get it into two angles that you know from the unit circle and take them seperately. which is how spikos homework i think wanted it done

Answer 38

sorry meant jimmy

Answer 39

yes - i just noticed i made a mistake in the last line

Answer 40

= 6pi - pi/2
=
= 5.5 pi
and sin 5.5pi = -1

Answer 41

awesome. thank you so much guys ;)

Answer 42

5.5pi - 2pi - 2pi = 3pi/2

Answer 43

The way I did it translates to

sin(11pi/2 - 4pi) = sin(11pi/2 - 8pi/2) = sin(3pi/2) = -1

Answer 44

yep

Answer 45

sin(11pi/2)=sin(10pi/2+1pi/2)=sin(5pi+pi/2)=sin(5pi)cos(pi/2)+sin(pi/2)cos(5pi)
=0*0+1*(-1)=-1