Question

Express in the form r sin(x-a)

sin x - sqrt(3) cos x

(worked solution please, I need to know the method :) )

Answer 1

if given an equation :
asinx + bsinx, it can be converting to r cos(x- θ)
with r = sqrt(a^2 + b^2)
to get θ, use defined of
tan θ = b/a

Answer 2

oppss. i mean if given asinx + bcosx

Answer 3

a is the coeff of sinx
b is the coeff of cosx

Answer 4

now, given sin x - sqrt(3) cos x
here a = 1 and b = - 1
so, the value of r = sqrt( 1^2 + (-1)^2) = sqrt(1+1) = sqrt(2)

Answer 5

then use defined
tanθ = b/a
tanθ = -1/1
θ = arc(tan(-1))

Answer 6

thanks anyway but i worked it out myself :) Thats why i closed it

Answer 7

because a has the value +ve(or rechall that the value of sin be (+), it means θ can be in the first quadrant or the 2nd quadrant), while b = -ve (or rechall that the value of cosine be (-), it means θ can be in the second quadrant or the 3rd quadrant)

now, most the quadrants for the θ is in the second quadrant.
so, θ is 135 degrees.
remember tan135 = -1

Answer 8

therefore, sin x - sqrt(3) cos x can rewriten becomes
sqrt(2) cos(x - 135)

Answer 9

you are incorrect :(

Answer 10

lol
which part, i have mistaken

Answer 11

dont worry man, i got it correct on my own. You dont have to waste your time :P

Answer 12

ahhh, you have edited ur equation :P
do you want it becomes r cos(x-a) OR r sin(x-a) ?????

Answer 13

it was always sin(x-a) ?

Answer 14

it can be r cos(x-a) OR r sin(x-a) , r tan(x-a), r sec(x-a), r csc(x-a), r cotan(x-a), which one do u like ??? :P

Answer 15

read the question, it asks for sin(x-a)!

Answer 16

before i read it was be r cos(x-a) --"

Answer 17

yours eyes must have fooled you