Answer
Cartesian equation: $y^2 - x^2 = 1, y \geq 1$ --------------
Work Step by Step
(a) $x =sinh \space t$
$x^2 = sinh^2 \space t$
$-x^2 = -sinh^2 \space t$
$y =cosh \space t$
$y^2 = cosh^2 \space t$
Adding both equations:
$y^2 - x^2 = cosh^2t-sinh^2t$
$y^2 - x^2 = 1$
- Notice, the parametric equation is only valid for $y \geq 1$, since $cosh \space t$ has a minimum value of $1$. Therefore, the cartesian equation should also have this condition: $y^2 - x^2 = 1, y \geq 1$ ----- (b) 1. Plot points determined by values for $t$.
I used -3, -2, -1, 0, 1, 2 and 3.
2. Join them to produce a curve.
3. Draw an arrow indicating which direction the curve goes from $t = -3$ to $t= 3$
