Question

Find cot θ of csc θ = (sqrt 5)/2 and tan θ > 0.

Answer 1

So like the last problem, let's figure out which quadrant we're in.

Answer 2

Tangent is positive again, so we must be in the 1st or 3rd.

Answer 3

1st

Answer 4

\[\large \csc\theta \qquad=\qquad \frac{1}{\sin\theta} \qquad=\qquad \frac{\sqrt5}{2}\]
First? Ok cool.

Answer 5

yes i got that far!!

Answer 6

\[\large \sin\theta=\frac{2}{\sqrt5}=\frac{opposite}{hypotenuse}\]

Understand what I did with our fraction there?

Answer 7

yes you got rid of the 1 on the numerator and had to flip the fraction to do so.

Answer 8

Yah some flippin.
Ok so let's draw our triangle.

Answer 9

okay

Answer 10

opp=2
hyp=sqrt5

Answer 11

Ok, cool.
So what's the missing side length? :D

Answer 12

1

Answer 13

so the answer is 1/2

Answer 14

thank you!

Answer 15

Yah that sounds right, good job.