Asked by Jamie

a) Find a linear approximation of y=sinx at x=pi/6

b) use part (a) to approximate sin(61pi/360) and sin(59pi/360)


I just really have no idea how to approach this problem. I know the formula is y=f(a)+f'(a)(x-a). Does that mean it would be (sin(pi/6))+(0)((pi/6)-(sin(pi/6))? Any help would be appreciated.

Answers

Answered by Reiny
"a) Find a linear approximation of y=sinx at x=pi/6 "
no linear approximation needed here, you MUST know that sin(π/6) = 1/2

for b) sin(61π/360)
= sin(60π/360 + π/360)
= sin(π/6 + (π/360)

so we will now use the formula that you stated:
f(x+a)=f(a)+f'(a)(x-a)
recall that if f(x) = sinx, then f '(x) = cosx
so let x = π/6 and a = π/360

sin(61π/360) = sin(π/6) + cos(π/6)*(π/360)
= 1/2 + (√3/2)(π/360)
= .507557

real answer: sin(61π/360) = .507538
error of .000019 , not bad

for the second part, note that 59π/360
= π/6 - π/360
so the last factor would be -π/360
and you should get .49244..
compared to the real answer of .49242..
(again, very close)
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions