Question

Rewrite sin x + cos x in the form k sin(x+a) I am LOST HELP ME!!!

Answer 1

sofar, i got up to this!!

Answer 2

but i dont know how to get (a)

Answer 3

ok here are my to cheat sheets, i hope they help

Answer 4

and try letting\[a=\sqrt{2}\]

Answer 5

why is it \[\sqrt{2}\] ??

Answer 6

okay the book said a=pi/4 but i dont know how it got the answer pi/4

Answer 7

sin(x+a) = sin(x)cos(a)+cos(x)sin(a)

Since we want

k*sin(x+a) = sin(x) + cos(x)

this means

k*sin(x+a) = k*(sin(x)cos(a)+cos(x)sin(a))

k*sin(x+a) = k*sin(x)cos(a)+k*cos(x)sin(a)

k*sin(x+a) = k*cos(a)*sin(x)+k*sin(a)*cos(x)

So k*cos(a) = 1 and k*sin(a) = 1

You can divide the two to get

(k*sin(a))/(k*cos(a)) = 1/1

tan(a) = 1

Answer 8

this is a little tricky !
you found that \[k=\sqrt{2}\]

Answer 9

\[\cos(a)=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\]
and \[\sin(a)=\frac{\sqrt{2}}{2}\]
so you need to know what is a ? right !

Answer 10

@lsugano

Answer 11

yess!

Answer 12

sorry my internet went down!!

Answer 13

you don't know how yet ?!

Answer 14

i dont know how to get (a) but in the book a=pi/4 which i dont know how they got that

Answer 15

yes ! did you see hamish93's attachements....trig cheat sheet ?!

Answer 16

yes i did!

Answer 17

take a look in "the unit circle" !

Answer 18

ok

Answer 19

i stilll dont get it :(

Answer 20

you need to commit this to your memory !

Answer 21

ok...

Answer 22

w8 ! I'll draw to you something !

Answer 23

ok! ah thank you so much!!!!

Answer 24

take a look ! at this !

Answer 25

\[\text{so } \frac{\pi}{4}<=====> 45°\]

Answer 26

OH i totally forgot that sin=y cos=x

Answer 27

makes much more sense!! thank so much for drawing it out for me!

Answer 28

you have to commit the unit Circl to your memory.....(the one in the Trig Cheat Sheet )

Answer 29

okay!! i will try my besttt!

Answer 30

Very Good :) !

Answer 31

thank you!!

Answer 32

im going to try another example like this could you please check if your not busy?

Answer 33

you're welcome !and I'm never busy !

Answer 34

the example ?!

Answer 35

i am almost done with my first step!!

Answer 36

so the question is y=sinx + √3cosx to the form ksin(x+a) a=radians

Answer 37

kk !

Answer 38

my first step looks like this!

Answer 39

now ! find "a" using the unit circle !

Answer 40

!!!!!!!

Answer 41

Very good ! that's correct !
you're brilliant ! :)

Answer 42

:) feels good to get the right answer! lol

Answer 43

since i was struggling with most of all the problems i feel happy right now/

Answer 44

yeaah :) :) and I feel happy for you !

Answer 45

thank you so much!!

Answer 46

:) It's been a pleasure ! :)