[a](adsbygoogle = window.adsbygoogle || []).push({}); Give a parametric equation for the line tangent to this curve at[itex]t = \frac{pi}{4}.[/itex]

[tex] \vec{r(t)} <e^tcost, e^tsint> [/tex]

Give the equation for this same tangent line in the form[tex]ax + by = c[/tex]

My attempt

[tex]\vec{r(\frac{pi}{4})} = <e^\frac{pi}{4}cos\frac{pi}{4}, e^\frac{pi}{4}sin\frac{pi}{4}[/tex]

[tex] = e^\frac{pi}{4}<\frac{1}{2}, \frac{1}{2}>[/tex]

[tex] \vec {r'(t)} = e^t<cost - sint, cost + sint>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<cos\frac{pi}{4} - sin\frac{pi}{4}, cos\frac{pi}{4} + sin\frac{pi}{4}>[/tex]

[tex] \vec {r'(\frac{pi}{4})} = e^\frac{pi}{4}<0,1>[/tex]

[tex] x = \frac{e^\frac{pi}{4}}{2} [/tex]

[tex] y = \frac{e^\frac{pi}{4}}{2} + e^\frac{pi}{4}t [/tex]

My answers aren't right. I suck.

Couldn't even solve for

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Parametric Equation for Tangent of Logarithmic Spiral

**Physics Forums | Science Articles, Homework Help, Discussion**