write x=sin theta, y= tan theta to eliminate theta.

Question

ash2326 · Answer

$$x=\sin \theta$$
$$y=\tan \theta$$
Divide first by second
$$\frac x y= \frac {\sin \theta}{\tan \theta}$$
@sophie14 what would you get on the right hand side?

anonymous · Answer

cos theta ?

ash2326 · Answer

good, so we have
$$\frac  x y =\cos \theta$$
Now there is an identity
$$\sin^2 \theta+\cos^2 \theta=1$$
Plugin the values of sin theta and cos theta, and voila!

anonymous · Answer

hmm I do not understand

ash2326 · Answer

$$\sin^2 \theta+\cos^2 \theta=1$$
sin theta= x
cos theta =x/y
so
$$x^2+\frac {x^2}{y^2}=1$$
so theta is eliminated, you can simplify this further

anonymous · Answer

how do you simplify this futher?

ash2326 · Answer

$$x^2(1+\frac 1 {y^2})=1$$
$$x^2(\frac{1+y^2}{y^2})=1$$
$$x^2=\frac{y^2}{1+y^2}$$

anonymous · Answer

thanks

anonymous · Answer

how do I get theta=     with sintheta= sin 15