If x=sin⁡t and y=cos⁡t, 0≤t≤π20≤t≤π2, eliminate t and write y as a function of x.

Question

would it be...

 

a. y=1-x^2
b.y=sqrt(x^2-1)
c. y=squrt(1-x^2)
d. none of these

Answer 1

I think that the question is:  eliminate t and express y as a function of x if x = sint and y = cost, where 0 ≤ t ≤ π/2.

 

Since 0 ≤ t ≤ π/2, x = sint ≥ 0 and y = cost ≥ 0

 

sin²t + cos²t = 1  So, x² + y² = 1

 

                                      y² = 1 - x²

 

                                      y = ±√(1-x²)

 

              Since y ≥ 0, y = √ (1-x²)  [Answer:  c]