Question

Are there any angles x and y that satisfy sin(x+y)=sinx+siny ? Use an example to explain your answer @kc_kennylau

Answer 1

Expand the LHS using the formulae hereeeee :)
http://www.a-levelmathstutor.com/images/trigonometry/ca-identities01.jpg

Answer 2

:(

Answer 3

Just changed the name of the variables, ain't a big deal xD

Answer 4

sin A + sin B

Answer 5

can you help me to replace x as A and y as B in the third formula? :)

Answer 6

I did ^^

Answer 7

the whole formula...

Answer 8

\[\sin(A+B)=\sin A\cos B+\cos A\sin B\]
Replace the whole formula, A->x and B->y

Answer 9

Sin(x+y)= sinxcosy+cosxsiny

Answer 10

exactly

Answer 11

yay :D

Answer 12

So can you substitute what you wrote to the left hand side of \(\sin(x+y)=\sin x+\sin y\)? :)

Answer 13

Idk

Answer 14

what you mean

Answer 15

So you have \(\sin(x+y)=\sin x\cos y+\cos x\sin y\) and \(\sin (x+y)=\sin x+\sin y\), what can you say about them? :)

Answer 16

that they're very similar :P

Answer 17

|(-_-)|

Answer 18

If \(a=b\) and \(a=c\), wha can you say about \(b\) and \(c\)?

Answer 19

its equal to A !!!

Answer 20

|(-_-)|

Answer 21

they can equal each other

Answer 22

:\

Answer 23

exactlyyyyyyyyyyyyyyyyyyyyyyyy :DDDDDDD

Answer 24

ohhhh

Answer 25

so can you summarize what I've just learned ?? thanks

Answer 26

So if \(\color{blue}{\sin(x+y)}=\color{red}{\sin x\cos y+\cos x\sin y}\) and \(\color{blue}{\sin(x+y)}=\color{green}{\sin x+\sin y}\), what can you say about \(\color{red}{\sin x\cos y+\cos x\sin y}\) and \(\color{green}{\sin x+\sin y}\)?

Answer 27

you've learnt that when the thing inside \(\sin\) or \(\cos\) is made up of two substances that are the same or different, you can always use the formulae hereeeeeeeeeeeeeeeeeeee xD
http://www.a-levelmathstutor.com/images/trigonometry/ca-identities01.jpg

Answer 28

omg not that link again >.<

Answer 29

but you have to memorize every. single. formula. of the website.......

Answer 30

yes yes

Answer 31

so the example we've used would be ???? what

Answer 32

would be the first formula used in the previous post, and the third formula being used now :D

Answer 33

what was the formula from the first tag ??

Answer 34

what do you mean first taggggg

Answer 35

first post !

Answer 36

you said it above

Answer 37

:'(

Answer 38

uh, it's the first formula \(\cos(A+B)=\cos A\cos B-\sin A\sin B\)

Answer 39

ok thanks for putting up with my lack of skils in math

Answer 40

:)

Answer 41

no problem :D

Answer 42

@kc_kennylau oh one more thing !

Answer 43

how would I convert the angle 4 to degrees???

Answer 44

\[\fbox{radian}=\fbox{degree}\times\frac\pi{180^\circ}\]\[\fbox{degree}=\fbox{radian}\times\frac{180^\circ}\pi\]

Answer 45

would it be 1pi/43?

Answer 46

@kc_kennylau

Answer 47

was the 4 in radian?

Answer 48

ikd it says convert following angles to degree measures

Answer 49

then i assume that it's radian

Answer 50

so is that the right answer that I got above?

Answer 51

nope :/

Answer 52

what is it?

Answer 53

The formula is \(\fbox{degree}=\fbox{radian}\times\dfrac{180^\circ}\pi\)

Answer 54

Substitute the \(\fbox{radian}\) as 4 :)

Answer 55

229.18

Answer 56

yep :)

Answer 57

thankss

Answer 58

:D<3

Answer 59

no problem <3