Question

Equation of tangent line

Answer 1

for an equation of a tangent line you need two things.......a point and the slope

Answer 2

I have the slope already right? So I'm supposed to find at what point there is a slope of 1/2?

Answer 3

y' = cosx

Answer 4

1/2 =cos x

Answer 5

x=pi/3

Answer 6

(π/3 , 1/2 ) - your point and the slope 1/2

Answer 7

find b in y=mx+b

Answer 8

Well first, what is the slope of a line? That's right! it is:

y = mx + b

now what is (m)? that's just the slope, which is just the derivative:

y = sin(x)

dy/dx = cos(x)

now it says you are looking for the point where dy/dx = 1/2, so why don't we go ahead and set 1/2 = cos(x). Now think back to you're trig, what does (x) have to be for cos(x) to be 1/2? Well just think of a 30-60-90 triangle and you should realize x=60 degrees, which is pi/3

1/2 = cos(x)

x = pi/3

So now we know use this x-value to find (m) and (b)

cos(pi/3) = 1/2

plug (pi/3) back into our original function to get the point we need to write out the line:

sin(pi/3) = sqrt(3) / 2

so you're line should now look like this

\[y - \sqrt(3) / 2 = (1/2) (x - \pi/3)\]

\[y = (1/2) (x - \pi/3) + \sqrt3 / 2\]

Answer 9

You guys are amazing at calculus lol

Answer 10

thanks for medals

Answer 11

^_^

Answer 12

Haha i'm not amazing, I was just like you once, grinding at giga-tons of Calculus homework.

Answer 13

here to help aren't we guys