Determine the ordered pair that lies on the unit circle corresponding to csc(5π/6). Thank you.
The wording of your question makes no sense to me.
Do you want csc(5π/6) as found on the unit circle?
We have an ordered pair associated with (5π/6) , not csc(5π/6)
I strongly suggest you print out one of the many unit circle diagrams available.
Here is one of them
https://www.google.ca/search?q=unit+circle+trigonometry&rlz=1C5CHFA_enCA690CA690&espv=2&biw=1660&bih=856&tbm=isch&imgil=b6OyxY_TLZ5-KM%253A%253BrinOamBJgRKAGM%253Bhttp%25253A%25252F%25252Fmathematica.stackexchange.com%25252Fquestions%25252F2456%25252Fgenerate-a-unit-circle-trigonometry&source=iu&pf=m&fir=b6OyxY_TLZ5-KM%253A%252CrinOamBJgRKAGM%252C_&usg=__HP98aavLGtFPfphMrS_Wm9xhprU%3D&ved=0ahUKEwiuwt603brOAhWLWxQKHTuoDDAQyjcIKA&ei=4iatV67JJou3UbvQsoAD#imgrc=b6OyxY_TLZ5-KM%3A
All ordered pairs are of the form (cosØ, sinØ)
since sin (5π/6) = 1/2
csc (5π/6) = 2
This is how the question appears.
Determine the ordered pair that lies on the unit circle corresponding to t=5pi/6. I'm sorry for the confusion.
That's not what you had originally.
Glad you changed it, now my solution should make sense to you.
To find the ordered pair corresponding to csc(5π/6) on the unit circle, we first need to determine the value of csc(5π/6).
Cosecant, denoted as csc, is the reciprocal of the sine function. So, to find csc(5π/6), we need to find the value of sine at 5π/6 and then take the reciprocal of that value.
First, let's determine the value of sine at 5π/6:
sin(5π/6) = sin(π - π/6)
Since sine is positive in the second quadrant, and in the second quadrant, the y-coordinate is positive, we can use the reference angle π/6 and look at the values for sine in the first quadrant on the unit circle.
In the first quadrant, the sine of π/6 is 1/2.
So, sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2.
Now, we need to take the reciprocal of 1/2 to find csc(5π/6):
csc(5π/6) = 1 / sin(5π/6) = 1 / (1/2) = 2.
Therefore, the value of csc(5π/6) is 2.
Now, let's determine the ordered pair on the unit circle that corresponds to csc(5π/6).
The unit circle represents points on a circle with a radius of 1.
Since csc(5π/6) is positive (from our earlier calculations), the point will lie in the first or second quadrant.
Since sine is positive and cosine is negative in the second quadrant, the cosine value for the angle 5π/6 is -√3/2.
So, the ordered pair corresponding to csc(5π/6) is (-√3/2, 2).
Therefore, the ordered pair that lies on the unit circle corresponding to csc(5π/6) is (-√3/2, 2).