Chapter 11.1, Problem 3QR

To determine

The equation relating $x$ and $y$ .

Answer to Problem 3QR

Therequired answer is $y^2=1-x^2$ .

Explanation of Solution

Given Information:

  $x=\sin t$  ........ (1)

  $y=\cos t$  ........ (2)

Calculation:

Squaring both equation

  $x^2={\sin }^{2}t$  ........ (3)

  $y^2={\cos }^{2}t$  ........ (4)

From equation (4)

  $\begin{array}{l}{y}^2={\cos }^{2}t\\ y^2=1-{\sin }^{2}t\end{array}$  ........ (5)

Substitute $x^2$ for ${\sin }^{2}t$ in equation (5)

  $y^2=1-x^2$

Conclusion:

Hence, the required answer is $y^2=1-x^2$ .