Question

Find sin A if sin4A=(2/3)

Answer 1

Hints:

sin(2x) = 2*sin(x)*cos(x)


cos(2x) = 1 - 2*sin^2(x)

and

sin(4A) = sin(2A+2A)

sin(4A) = sin(2A)cos(2A) + cos(2A)sin(2A)

sin(4A) = 2*cos(2A)sin(2A)

Answer 2

It's not complete, but I'll let you finish up

Answer 3

i got that far. i'm just confused on the rest of the way.

Answer 4

I got to 4sinAcosA(1-2sin^2A)=2/3. I just don't know how to convert this into a form for sin A.

Answer 5

hmm let me think

Answer 6

well it's really ugly, but I'll try my best to explain

Answer 7

we know that sin(4A) = 2/3

so let's isolate A first

Answer 8

sin(4A) = 2/3

4A = arcsin(2/3)

A = (1/4)*arcsin(2/3)


now we want to find sin(A), so apply the sine function to both sides to get

sin(A) = sin((1/4)*arcsin(2/3))

Answer 9

with me so far?

Answer 10

yeah, it's been a while since i did arcsin but it should be easy for me to review. go on.

Answer 11

wait arcsin is the inverse, isn't it? i'll try to solve the problem soon but if i have troubles i'll let you know. i'll put up my answer and steps regardless

Answer 12

yes arcsine is the inverse of sine

Answer 13

and from here, you will use the half angle identities which are

cos(x/2) = sqrt( (1+cos(x))/2 )
sin(x/2) = sqrt( (1-cos(x))/2 )

Answer 14

i appreciate it very much, thanks for the help

Answer 15

yw