Better Students Ask More Questions.
find the equation of the line tangent to the graph of sin(x) at the following value of...
1 Answer | add yours
You should find the equation of the tangent line, to the graph of function `y = sin x` , at the point `x = 4pi` , such that:
`y - sin(4pi) = (dy)/(dx)|_(x = 4pi)(x - 4pi)`
You need to evaluate ` sin 4pi` using the following trigonometric identity, such that:
`sin 4pi = sin 2*(2pi) = 2 sin 2pi*cos 2pi`
Since `sin 2pi = 0` yields:
`sin 4pi = 0`
You need to evaluate the derivative of the function `y = sin x` such that:
`(dy)/(dx) = cos x => (dy)/(dx)|_(x = 4pi) = cos 4pi = cos^2 2p` i
Since `cos 2pi = 1` yields:
`cos 4pi= 1`
Replacing 0 for `sin 4pi` and 1 for `cos 4pi` yields:
`y - 0 = 1*(x - 4pi) => y = x - 4pi`
Hence, evaluating the equation of the tangent line to the graph of function `y = sin x` , at the point `x = 4pi` , yields `y = x - 4pi.`
Posted by sciencesolve on June 26, 2013 at 5:20 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.