If-x-3sin-x-2-y-2-and-y-4cos-find-cos-

Question Number 6370 by sanusihammed last updated on 25/Jun/16

I f x = \frac{3 s i n θ}{\sqrt{x^{2} + y^{2}}} a n d y = 4 c o s θ

f i n d c o s θ

Commented by nburiburu last updated on 25/Jun/16

c o s θ = y / 4 w i t h 16 x^{2} (x^{2} + y^{2}) + 9 y^{2} = 144

Commented by sanusihammed last updated on 25/Jun/16

W h a t i s t h e f i n a l a n s w e r .

Commented by prakash jain last updated on 25/Jun/16

\sin θ = a

\cos θ = b

You have followinh equations

x = \frac{3 a}{\sqrt{x^{2} + y^{2}}}

y = 4 b

a^{2} + b^{2} = 1

So with 4 variables you have only 3 equations .

The information is not complete .

Commented by FilupSmith last updated on 25/Jun/16

∴ x = \frac{3 \sin θ}{\sqrt{x^{2} + 4^{2} \cos^{2} θ}}

∴ x^{2} (x + {16 \cos}^{2} θ) = 3 \sin θ

x^{3} + 16 x^{2} (1 - \sin^{2} θ) = 3 \sin θ

x^{3} + 16 x^{2} - 16 x^{2} \sin^{2} θ = 3 \sin θ

continue to transpose for θ

a n d s o l v e \cos θ