You are here:

Question
I am stumped on this question (super-nerd myself, working ahead in my textbook just for fun), but was hoping you could explain your answer and how you got it on this one.

Given f(x)=sin(x)
Find:
Part A) the slope of f(x) at x=pi
Part B) write an equation for the tangent to f(x) at x=pi
Part C) write an equation for the normal line to f(x) at x=pi

Sin(x)
Hi John,
Perhaps it would have been helpful if you told me exactly what you're having problems with or the level at which you're studying. Anyway, for a function f(x) we can find its slope f'(x) (read f prime x) by differentiating the function.
Given f(x) = sin(x)
The slope f'(x) = cos(x)
At x = π, the slope of f(x) (which is the slope of the tangent line at x = π) then has a value of cos(π) = -1

As we know from coordinate geometry, we can write the equation of a line with a slope m which passes through a point (x1, y1) as;
(y - y1)/(x - x1) = m
So,
m = -1
x1 = π
y1 is the value of f(x) at x1 i.e sin(π) = 0
The equation is then
(y - 0)/(x - π) = -1
y = π - x

Again from coordinate geometry, if two lines are perpendicular then the product of their slope is -1. Taking the slope of the normal line as k, we must have that
mk = -1
k = -1/m = -1/-1 = 1
The normal line also passes through the same point (π, 0) and so its equation is
(y - 0)/(x - π) = 1
y = x - π

Regards
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment No Comment

Volunteer

Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

Aspiring theoretical physicist. I have been doing maths and physics all my life.

Education/Credentials
I teach mathematics and engineering physics.