Question

HELP!!
If sinθ=2/3 , find the values of the other five trigonometric functions of θ .

Answer 1

According to basic trig, \[\sin \theta=\frac{ y }{ r }\]

So we know right away that \[y=2\] \[x=3\]

You can use Pythagorean Theorem to determine the value of x \[x=\sqrt{r ^{2}-y ^{2}}\]

Then you can use the given values to determine the other 5 ratios:
\[\cos \theta =\frac{ x }{ r }\]
\[\tan \theta =\frac{ y }{ x }\]
\[\csc \theta =\frac{ r }{ y }\]
\[\sec \theta =\frac{ r }{ x }\]
\[\cot \theta =\frac{ x }{ y }\]

Answer 2

My apologies, the 5th line should say \[r=3\]

Answer 3

Next time, Blue, let's see some of YOUR work.

Answer 4

@tkhunny I didn't know how to do it that's why I asked......?

Answer 5

@colinvda give me a second and I'm going to put the answers I got and can you check over them?

Answer 6

That's not an acceptable excuse. You MUST have SOMETHING. If you have NOTHING, you are either not attending class or you are in the wrong class. Do better. Show YOUR work. No excuses.

Answer 7

So @colinvda I got x=6?

Answer 8

I don't think so, double-check your calculations.

Answer 9

oops!! is it sqrt5?

Answer 10

Yes it is! Now you have all the values you need to fill out the trig values!

Answer 11

\[\cos \theta =\sqrt{5}/3 \tan \theta =2/\sqrt{5} \csc \theta =3/2 \sec \theta =3/\sqrt{5} \cot \theta =\sqrt{5}/2\]

Answer 12

is that right? @colinvda

Answer 13

Looks good to me!

Answer 14

Thanks :) @colinvda