# Help angle of inclination

• Sep 20th 2012, 02:55 PM
pnfuller
Help angle of inclination
how do you calculate the angle of inclination of y=x2 to the nearest degree?

• Sep 20th 2012, 03:21 PM
HallsofIvy
Re: Help angle of inclination
A function does not have an "angle of inclination"! I assume you mean "the angle of inclination with the x-axis of the tangent to the curve $y= x^2$ at any point".

If $\theta$ is the angle the tangent line to y= f(x) makes with x-axis than $tan(\theta)= df/dx$.
• Sep 20th 2012, 04:59 PM
pnfuller
Re: Help angle of inclination
so what am i suppose to do with that? the answer is 63 degrees but how do i get that?
• Sep 20th 2012, 05:55 PM
pnfuller
Re: Help angle of inclination
Quote:

Originally Posted by HallsofIvy
A function does not have an "angle of inclination"! I assume you mean "the angle of inclination with the x-axis of the tangent to the curve $y= x^2$ at any point".

If $\theta$ is the angle the tangent line to y= f(x) makes with x-axis than $tan(\theta)= df/dx$.

so what am i suppose to do with that? the answer is 63 degrees but how do i get that?
• Sep 20th 2012, 06:05 PM
skeeter
Re: Help angle of inclination
Quote:

Originally Posted by pnfuller
how do you calculate the angle of inclination of y=x2 to the nearest degree?

please post the entire problem as stated from its source ... I've never heard of the angle of inclination of a function, either.
• Sep 20th 2012, 06:41 PM
pnfuller
Re: Help angle of inclination
let l be the tangent line to the parabola y=x^2 at the point (1,1). the angle of inclination of l is the angle θ that l makes with the positive direction of the x-axis. calculate θ correct to the nearest degree. i know the answer should be 63 degrees but how?
Quote:

Originally Posted by skeeter
please post the entire problem as stated from its source ... I've never heard of the angle of inclination of a function, either.

• Sep 20th 2012, 06:54 PM
MarkFL
Re: Help angle of inclination
The slope of the tangent line is found by evaluating the derivative of the function at the given x-coordinate.

$y'(1)=2(1)=2$

The slope $m$ of a line is related to its angle of inclination $\theta$ by $m=\tan(\theta)$.

Hence, the angle of inclination is $\theta=\tan^{-1}(2)\approx63^{\circ}$.