Question

sin (2sin^-1(x) PLEASE HELP BIG MATH TEST TOMRW

Answer 1

I'm going to use arcsin(x) instead of sin^-1(x)

Let y = arcsin(x) which means sin(y) = x/1

so

sin(2*arcsin(x)) = sin(2y)

Use the identity sin(2x) = 2*sin(x)*cos(x) to get

sin(2y) = 2*sin(y)*cos(y)

Now we turn to a drawing of a right triangle

Answer 2

cos(y) = adj/hyp = sqrt(1-x^2)/1 = sqrt(1-x^2)

Answer 3

So...

sin(2y) = 2*sin(y)*cos(y)

sin(2y) = 2*x*sqrt(1-x^2)

sin(2*arcsin(x)) = 2*x*sqrt(1-x^2)

Answer 4

i seriously might fail tomorrow but thank you so much for your help

Answer 5

is this all looking completely foreign to you?

Answer 6

no i'm really good with trig identities, i'm just lost when solving equations. i solved this question right but it looked wrong so i thought i needed help

Answer 7

so the identity sin(2y) = 2*sin(y)*cos(y) looks familiar?

Answer 8

yes thank you

Answer 9

So what you need to do is go from sin(2*arcsin(x)) to sin(2y)

Then break that up into 2*sin(y)*cos(y)

Answer 10

then use the diagram to find sin(y) and cos(y)

sin(y) is already given based on how you defined y

since y = arcsin(x), this means sin(y) = x