Asked by Anonymous
Use the function defined below to find an equation of the tangent line at the point indicated.
y = cos(x), x = π/3
y = cos(x), x = π/3
Answers
Answered by
Reiny
I don't see a definition defined below, but .....
when x = π/3 , y = cosπ/3 = 1/2
so the point is (π/3, 1/2)
slope = y' = sinx = sinπ/3 = √3/2
equation of tangent:
y = (√3/2)x + b
at (π/3,1/2)
1/2 = (√3/2)(π/3) + b
b = 1/2 - π√3/6 = (3 - π√3)/6
replace b with that, and you are done
when x = π/3 , y = cosπ/3 = 1/2
so the point is (π/3, 1/2)
slope = y' = sinx = sinπ/3 = √3/2
equation of tangent:
y = (√3/2)x + b
at (π/3,1/2)
1/2 = (√3/2)(π/3) + b
b = 1/2 - π√3/6 = (3 - π√3)/6
replace b with that, and you are done
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