Homework Help Calculus
Find the linear approximation L(x)of the function f(x)=cos(pi/(6)x) at the point x=1 and use it to estimate the value of cos(13pi/72).
Here's what I did so far:
L(x)=sqrt(3)/21/12pi(x1)+0((x1)^2)
How do I find cos(13pi/72)
asked by
Amy

f' = pi/6 sin(pi/6 x)
f'(1) = pi/6 (1/2) = pi/12
f(1) = √3/2
So, the tangent line is
y√3/2 = pi/12 (x1)
13pi/72 = pi/6 (13/12)
So, plug in x=13/12 into the equation of the line. Note that 13/12 is close to 1, so the approximation should be close to cos(13pi/72)
which you can get using any scientific calculator.posted by Steve
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