Question

Consider the right triangle shown below that has side lengths of x, y and r units.For each of the following questions, write an expression in terms of θ that answers the question. Enter "theta" for θ.y is how many times as large as r? ____times as large   x is how many times as large as r? _____times as large   y is how many times as large as x? ___times as large

Answer 1

Determine relation between side of triangle by using trigonometry.

`\begin{gathered} \sin \theta=(y)/(r) \\ y=r\sin \theta \end{gathered}`

So y is sin theta times as large as r.

`\begin{gathered} \cos \theta=(x)/(r) \\ x=r\cos \theta \end{gathered}`

So x is cos theta times as large as r.

`\begin{gathered} \tan \theta=(y)/(x) \\ y=x\tan \theta \end{gathered}`

So y is tan theta times as lasrge as x.