Question

If x=3sinA and y=4cosA then find the value of √16x²+9y²

Answer 1

√16x2+9y2
4x2+9y2
4(3sinA)2+9(4cosA)2
4(9sin2A)+9(16cos2A)
36sin2A+144cos2A

Answer 2

Hey there,



Given:
$x = 3 \sin \: a \:$
$y = 4 \cos \: a$


To find,

$\sqrt{16 ({x}^{2}) + 9 {(y)}^{2} }$


Substitute the values you have in,

$\sqrt{(16 {(3sin \: a)}^{2}) + 9 {(4\cos \: a) }^{2} } \\ \\ \\ = \sqrt{(16)(9) { \sin }^{2}a + (9)(16) { \cos }^{2}a } \\ \\ \\ = \sqrt{(16)(9)( { \sin }^{2}a + { \cos }^{2} a })$


As you might me familiar with:
${ \sin }^{2} x + { \cos }^{2} x = 1$

Using this identity,
we'll be left with,

$= \sqrt{(16)(9)} \\ \\ =4 \times 3 \\ = 12$


Therefore your required answer will be 12.