i6.4 If $$ x=3 \sin heta $$ and $$ y=3 \cos heta $$. detennine the value of $$ x^{2}+y^{2} $$

Question

i6.4 If $$ x=3 \sin 	heta $$ and $$ y=3 \cos 	heta $$. detennine the value of $$ x^{2}+y^{2} $$

UpStudy AI · Accepted Answer

1. Substitute the given values into the expression:
   $$
   x^2 + y^2 = (3\sin \theta)^2 + (3\cos \theta)^2
   $$

2. Square the terms:
   $$
   x^2 + y^2 = 9\sin^2 \theta + 9\cos^2 \theta
   $$

3. Factor out the common factor:
   $$
   x^2 + y^2 = 9(\sin^2 \theta + \cos^2 \theta)
   $$

4. Use the Pythagorean identity:
   $$
   \sin^2 \theta + \cos^2 \theta = 1
   $$

5. Substitute the identity into the expression:
   $$
   x^2 + y^2 = 9 \times 1 = 9
   $$

Therefore, the value of $$ x^2+y^2 $$ is $$ 9 $$.
$$ x^{2} + y^{2} = 9 $$

i6.4 If \( x=3 \sin \theta \) and \( y=3 \cos \theta \). detennine the value of \( x^{2}+y^{2} \)