Question

Find the value of tan θ for the angle shown.

Answer 1

\[
\tan \theta =\frac{\sin \theta}{\cos\theta}
\]

Answer 2

tan ratio in cartesian is defined by just y/x

Answer 3

\[
(\cos\theta,\sin\theta) = (\sqrt{33},-4)
\]

Answer 4

tan theta = y co-ordinate/ x co-ordinate

Answer 5

So it would be sqrt 33/4 all negative?

Answer 6

\(\color{blue}{\text{Originally Posted by}}\) @wio
\[
\tan \theta =\frac{\sin \theta}{\cos\theta}
\]
\(\color{blue}{\text{End of Quote}}\)
\(\color{blue}{\text{Originally Posted by}}\) @wio
\[
(\cos\theta,\sin\theta) = (\sqrt{33},-4)
\]
\(\color{blue}{\text{End of Quote}}\)
\[
\tan\theta = \frac{-4}{\sqrt{33}}
\]

Answer 7

no...the numerator is actually y co-ordinate

Answer 8

you know what a y co-ordinate is ?

Answer 9

The answer above is not one of my options.
These are my options.


tan θ = - sqrt33/4

tan θ = - 4sqrt33/33

tan θ = - 4/7

tan θ = - sqrt33/7

Answer 10

you will have to rationalize the denominator, know how to ?

Answer 11

I do not, this is just a practice problem so im trying to see how to get the answer so i can try others on my own.

Answer 12

ok, sqrt 33 is an irrational number
to rationalize it, multiply it by another sqrt 33

Answer 13

\[
\frac{-4}{\sqrt{33}} = \frac{-4}{\sqrt{33}} \times \frac{\sqrt{33}}{\sqrt{33}}= \frac{-4\sqrt{33}}{33}
\]

Answer 14

but when you multiply sqrt 33 in the doniminator, you will have to multiply it in numerator too

Answer 15

like what @wio did

Answer 16

Ohhhhhhhh thats why -4/sqrt33 wasnt one of my answers! Thanks i got it now!