## Multivariable Calculus, 7th Edition

a) $y= cos(sin^{-1}x)$ or $x^{2}+y^{2}=1$, $y \geq 0$ b) (Graph) As θ increases, x increases and y increases to 1, then decreases to 0.
a) $x= sin(\frac{1}{2}θ)$ $y= cos(\frac{1}{2}θ)$ $-π \leq θ \leq π$ $x= sin(\frac{1}{2}θ)$ $2sin^{-1}x=θ$ $y= cos(\frac{1}{2}θ)$ $y= cos(\frac{1}{2}2sin^{-1}x)$ $y= cos(sin^{-1}x)$ which is the same as, $x^{2}+y^{2}=1$, $y \geq 0$ b) When, θ=-π x=-1 y=0 θ=-π/2 $x=-(\sqrt 2)/2$ $y=(\sqrt 2)/2$ θ=0 x=0 y=1 θ=π/2 $x=(\sqrt 2)/2$ $y=(\sqrt 2)/2$ θ=π x=1 y=0 From this we can infer that as θ increases, x increases and y increases to 1, then decreases to 0.