Graphing parametric curves

Question

x= sin(1/2)θ 

 

y=cos(1/2)θ 

 

-pi≤θ≤pi

 

Im not understanding the interval and how this graph is going to look like.

Answer 1

sin²(θ/2) + cos²(θ/2) = 1

 

So, x² + y² = 1  (this is the circle centered at (0,0) with radius 1)

 

When θ = -π, x = -1 and y = 0

When θ = 0, x = 0 and y = 1

When θ = π, x = 1 and y = 0

 

The given parametric equations and limits on θ trace out the upper half of the unit circle starting at (-1,0).