- #1

- 36

- 2

## Homework Statement

x=sec(t),

y=tan(t),

-π/2 ≤ t ≤ π/2

Try to find y in terms of x

## Homework Equations

## The Attempt at a Solution

1.[/B]

∂y/∂x = sec(t)/tan(t)

y=∫sec(t)/tan(t)∂x

=∫x/y∂x

=(1/y)*∫x∂x

=x

^{2}/2y + C

2y

^{2}=x

^{2}+ C

When t=π/4, x=√2, y=1

2(1)

^{2}= (√2)

^{2}+ C

C=0

So y

^{2}= x

^{2}/2

2.

y/x = sin(t)

1/x = cos(t)

sin

^{2}(t) + cos

^{2}(t) = 1

y

^{2}/x

^{2}+ 1/x

^{2}= 1

y

^{2}= x

^{2}+ 1

Why couldn't I get the same equations in both (1) and (2)? It turns out only the equation 2 works well with other value of t. What did I do wrong in (1)?