Question

Will Medal! Pre Calc help
If csc Θ=0.8 and 270°<Θ<360°, find the exact value of sin 2Θ.

Answer 1

Hi @UsernameNotTaken
ready to solve it?

Answer 2

ok

Answer 3

@Astrophysics s/he should know that this problem is incorrect. shouldn't s/he?

Answer 4

I was afk doing other problems, sorry for not being here in time.

Answer 5

Yes i did make a mistake... The correct version is
cos Θ=0.8 and 270°<Θ<360°, find the exact value of sin 2Θ.

Answer 6

Ok better, so \[\sin 2 \theta = 2 \sin \theta \cos \theta \]

Answer 7

:)

Answer 8

xD yeah sorry, he he he...

Answer 9

Do you know how to find sin theta?

Answer 10

my answer is -0.96 but i think its wrong..

Answer 11

@astrophysics yes i do

Answer 12

I think your answer maybe ok, lets keep going and see if it's right or not

Answer 13

So what did you get for sin theta?

Answer 14

Why do you think so?
Explain how you solved it and @Astrophysics and me can check it.
ur answer's correct.

Answer 15

Thanks @Yavar

Answer 16

270° < θ < 360°, θ is in Quadrant III. so sinθ < 0.

By drawing a 3-4-5 triangle in Quadrant III such that cosθ = 3/5, we see that:
adj = 3, opp = 4, and hyp = 5 ==> sinθ = -opp/hyp = -4/5.

Therefore, by the double-angle formula for sine:
sin(2θ) = 2sinθcosθ
= 2(-4/5)(3/5)
= -24/25. or -0.96

Answer 17

That was basically it in a nutshell....

Answer 18

Hey, that looks good!

Answer 19

That was nice.....