Question

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

Answer 1

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

Answer 2

cos theta ?

Answer 3

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!

Answer 4

hmm I do not understand

Answer 5

\[\sin^2 \theta+\cos^2 \theta=1\]
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

Answer 6

how do you simplify this futher?

Answer 7

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

Answer 8

thanks

Answer 9

how do I get theta= with sintheta= sin 15