Question

If \(cos\theta=-\frac{2}{3}\), which of the following are possible?

A: \(csc\theta=\frac{3}{\sqrt{5}}\) and \(tan\theta=-\frac{\sqrt{5}}{2}\)

B: \(sin\theta=\frac{\sqrt{5}}{3}\) and \(tan\theta=\frac{\sqrt{5}}{2}\)

C: \(csc\theta=-\frac{3}{2}\) and \(tan\theta=\frac{\sqrt{5}}{2}\)

D: \(sin\theta=-\frac{\sqrt{5}}{3}\) and \(tan\theta=\frac{\sqrt{5}}{2}\)

Answer 1

@dude @563blackghost

Answer 2

I hope I dont get in trouble for this
A: \(csc\theta=\frac{3}{\sqrt{5}}\) and \(tan\theta=-\frac{\sqrt{5}}{2}\)

Answer 3

Is that the only one?

Answer 4

There are multiple answers?

Answer 5

I only assume there is one answer
"which of the following" refers to a single answer since it contains 2 equations

Answer 6

Ah, well more then one can be correct in this case.

Answer 7

Well from my assumptions I have
Opposite = \(\sqrt{5}\)
Adjacent = 3
Hypotenuse = -2

Answer 8

Does that mean only that one is correct?

Answer 9

Hold up I am trying to make all the equations x'D

Answer 10

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
Well from my assumptions I have
Opposite = \(\sqrt{5}\)
Adjacent = 3
Hypotenuse = -2
\(\color{#0cbb34}{\text{End of Quote}}\)
Mistake here
Flip Hypotenuse and Adjacent

Answer 11

\(sin(\theta)= \frac{\sqrt5}{3}\)

\(tan(\theta)= \frac{\sqrt5}{-2}\)

\(csc(\theta)= \frac{3}{\sqrt5}\)

Answer 12

I am unsure of my signs

Answer 13

Alright... if I'm understanding that right...

Only A is right?

Answer 14

I am unsure, I need to check for my signs

Answer 15

Use this "Cast" rule for the signs of trig functions in the 4 Quadrants:

Answer 16

@sillybilly123 you couldve just answered the q x.x

Answer 17

because cosine is -ve you know it is this:



or this:

Answer 18

i am totally sure you can take it from there