Question

Linear approximation help: I need to show via tangent line approximation at 0 to show that sinx=x near 0 is a good approximation. Then I need to give the amount of error using the approximation at x=pi/6

Answer 1

what do you know about a tangent line?

Answer 2

Would I be finding the tangent line of sin(x) at x=0?

Answer 3

If so it's just y=x, which would show that 0=0 for both, which makes it a good approximation?

Answer 4

yes, the tangent line at x=0 will give us a model to approximate answer that are close to sin(x=0)

Answer 5

So then the error with pi/6 would be sin(pi/6)=pi/6, which is .5=.5235987756, so the error is just actual over theoretical?

Answer 6

the amount of error, i read this as the difference between actual and predicted

sin(0) - pi/6 = amount of error

the percentage of error is a division: difference/actual

Answer 7

spose we have some line function: f(x) = mx + b, in order for this to model sin(x) they have to have the same derivatives

sin(x) = mx + b

cos(x) = m; cos(0) = m

sin(0) = b

so yes: sin(x) is about y=x

Answer 8

ok thank you for your time

Answer 9

youre welcome