Question

Apply the sum and difference formula for sine to simplify the left hand side of the equation

sin(x+pi/4) - sin(x-pi/4)=1

Answer 1

Will medal!!!!

Answer 2

umm...whut grade r u in?

Answer 3

Why?

Answer 4

jw

Answer 5

12th. Senior

Answer 6

You?

Answer 7

like this i think
sin(A+B) = sin (A)* cos (B) + sin (B) cos (A)

sin(A-B) = sin (A) * cos (B) - sin (B) cos (A)

therefore,

sin(x+pi/4)+sin(x-pi/4) = sin(x)cos(pi/4)+sin(pi/4)cos(x) + sin(x)cos(pi/4)-sin(pi/4)cos(x)
= 2*sin(x) cos(pi/4)

Now, cos(pi/4)=cos(45 degrees) = 1/sqrt(2).

Therefore

sin(x+pi/4)+sin(x-pi/4)=2*(1/sqrt(2))*... = sqrt(2) * sin(x)

and finally, we make this equal to 1:

sin(x+pi/4) +sin(x-pi/4) = sqrt(2) sin(x) = 1

therefore the x's that solve this will be:

sin(x)=1/sqrt(2) --> x=pi/4, 3pi/4, 9pi/4, 11pi/4, 15pi/4, 17pi/4, and also -7pi/4, -5pi/4, -13pi/4, -15pi/4...etc

in general:

x= pi/4 (plus minus) 2*pi

and

x = - pi/4 (plus minus) 2*pi

the "plus minus" 2*pi is considering any number of cycles you want to make around the unit circle.

Answer 8

does that help

Answer 9

@csheveland does that help

Answer 10

It does. I am sorry but that Is almost an identical match to the yahoo answer I found. Hmmm.

Answer 11

thnx!!

Answer 12

it is the yahoo answer and i am in 9th

Answer 13

I am graduating at 16 though. So technically I'm a 10th grader. Anyway, thank you for the help.

Answer 14

I did not mean to sound rude.

Answer 15

u r very welcome and u didnot sound rude u were asking a question r u n vertual school

Answer 16

I suck at school doesn't quite fit you......

Answer 17

haha thx if u wanna talk msg me so i can help my friend ok? thx lol

Answer 18

and get off of this one

Answer 19

Sorry. Thnx.

Answer 20

ur very welcom