## anonymous 5 years ago how is x=tanθ when using trig sub

1. anonymous

For (a^2+x^2), you substitute x = a tan (theta) because when you replace the equation a^2 + x^2 with a^2 + (a tan (theta))^2, you get a^2 ( 1 + tan^2 (theta)) which becomes a^2 (sec^2 (theta)).

2. anonymous

I'm trying to figure out when solving for arc length r=e^θ from (1,0) to origin, you have to convert the limits in terms of theta. I found that someone used tanθ = x to solve the problem. I'm wondering how the person got the equation.

3. anonymous

For arc length, can you use the equation $\int\limits_(\sqrt(1+(f'(x))^2)$ from a to b?

4. anonymous

∫ab sqrt (r^2 + (dr/dθ)^2) dθ is what i used

5. anonymous

Are you doing it in polar?

6. anonymous

yes

7. anonymous

You are integrating dθ - so you need the limits in the integral to be in terms of theta.

8. anonymous

http://tutorial.math.lamar.edu/Classes/CalcII/PolarArcLength.aspx i'm confused about the trig sub that he used to convert the limits

9. anonymous

Well you'd still use a a tan $\theta$ because it will simplify if you use trig identities.

10. anonymous

$a \tan(\theta)$

11. anonymous

but how is tanθ = x or y

12. anonymous

isnt it tanθ = y/x?