Question

Which of the following angles is in the solution set of csc^2θ - cscθ - 20 = 0 for 0° ≤ θ < 360°
ans:14.5°,165.5°,168.5°,348.5°

Answer 1

Factor out csc theta
Can you do that?

Answer 2

Oh> Just a minute. Your post isn't clear. Why don't you retype it and use x for the angle. Then it might be clearer.

Answer 3

is it really -20?

Answer 4

\[\csc ^2\theta-\csc \theta-20=0\]

Answer 5

yes it is

Answer 6

Is that it?

Answer 7

\[x^2-x-20=0\]

Answer 8

yes

Answer 9

Which has these factors:
\[(x-5)(x+4)=0\]

Answer 10

So we have:
\[(\csc \theta-5)(\csc \theta+4)=0\]

Answer 11

\[\csc \theta=5 and \csc \theta=-4\]

Answer 12

i put the answer options under the question.

Answer 13

so
\[\sin \theta=\frac{1}{5}\]

Answer 14

and
\[\sin \theta=-\frac{1}{4}\]

Answer 15

So put those values into your calculator and hit the inverse sin button

Answer 16

it doesnt come out to any of the answers

Answer 17

What did you get when you put in -1/4?

Answer 18

the sin of -1/4 is -0.004363309 and the inverse is -0.25

Answer 19

Find \[\sin ^{-1}(.2)\]

Answer 20

Then find
\[\sin ^{-1}(-.25)\]

Answer 21

i got 11.53695903 and then -14.47751219

Answer 22

in radian mode i got 0.201357921 and -0.252680255 the other was in degree mode