Find the cartesian equation of the curve whose parametric equations are :
`x=4"cos"theta, y=4"sin"theta`

Answer

To find the Cartesian equation of the curve given the parametric equations \( x = 4 \cos \theta \) and \( y = 4 \sin \theta \), we will follow these steps:

### Step 1: Write down the parametric equations
We have:
1. \( x = 4 \cos \theta \) (Equation 1)
2. \( y = 4 \sin \theta \) (Equation 2)

### Step 2: Square both equations
We square both equations to eliminate the trigonometric functions:
- Squaring Equation 1:
\[ x^2 = (4 \cos \theta)^2 = 16 \cos^2 \theta \quad \text{(Equation 3)} \]
- Squaring Equation 2:
\[ y^2 = (4 \sin \theta)^2 = 16 \sin^2 \theta \quad \text{(Equation 4)} \]

### Step 3: Add the squared equations
Now, we add Equation 3 and Equation 4:
\[ x^2 + y^2 = 16 \cos^2 \theta + 16 \sin^2 \theta \]
Factoring out the common term on the right side gives:
\[ x^2 + y^2 = 16 (\cos^2 \theta + \sin^2 \theta) \]

### Step 4: Use the Pythagorean identity
We know from trigonometric identities that:
\[ \cos^2 \theta + \sin^2 \theta = 1 \]
Substituting this identity into our equation:
\[ x^2 + y^2 = 16 \cdot 1 \]
Thus, we simplify to:
\[ x^2 + y^2 = 16 \]

### Conclusion
The Cartesian equation of the curve is:
\[ \boxed{x^2 + y^2 = 16} \]