Trigometry Help! 10 points best answer

Question: 2csc^2x=4 I need to find the solution set, 0 to 360, and the problem is I get to

2csc^2x=4
csc^2x=2
and I don't know what to do from here, can you also tell me if my steps are correct. thank you.

Hello,

Yes you are right at the beginning

Csc²(x) = 2
Then
Csc(x) = +√2 or -√2

What is Csc ? it is the inverse of sine

1/sin(x) = +√2 or -√2

sin(x) = 1/√2 or -1/√2

Your calculator or your memory will tell you that

Arcsin (1/√2) = 45°
The trigonometric circle shows you that 180° - 45° = 135° has the same sine (check on calculator)

Arcsin (-1/√2) = - 45° = 360 - 45 = 315°
The trigonometric circle shows you that 180° - (-45°) = 225° has the same sine (check on calc.)

Then the set of solutions is { 45° ; 135° ; 225° ; 315° }

Hope it helped !

Bye !

yeah, you're correct so far....but what you should do,
cosec(x)=2
Remember cosec(x)= 1/sin(x),
is the same as {cosec(x)}^2= (1/sin(x)}^2

1/ sin^2(x)=2

cross multiply to get
1=2sin^2 (x)
1/2= sin^2(x)
Sin(x) = √(1/2)(a calculator would help here,haha)

it will be, (x)= sin (+√o.5 or -√0.5)
(you will get 2 values for +√o.5 and -√0.5 each because it will be where sin has positive and negative angles)(positive lies in 0-90 and 90-180, where as negative lies in 180-270 and 270-360 degrees)
just subtract your angles in positive region to 270 and 360

x= 45° ; 135° ; 225° ; 315°
Hope this helped...........did it a while aback

I csc^2 x = 2, then sin^2 x = 1/2 and sin x = ± 1/√2, which means that x = 30°, 150°, 210° or 330°.

x = 45 || x = 135 || x = 225 || x = 315