Question

I already input the answers, I just need help explaining these 3 similar problems thoroughly

http://prnt.sc/d9rzvy
"1. Determine the exact value using the unit circle. Explain how you arrived at your answers"

Answer 1

do you can show your work how you ve got these results ?

Answer 2

exactly, i used Mathway - i understand the answer, i just need help explaining how to do the work

Answer 3

im not good at explaining stuff :/

Answer 4

ok hope i can help you - like a first step try using mathway what used before just write there to calculi on the first step sin pi/3

ok. ?

Answer 5

it doesn't explain anything other than what i have written down, i have to pay for the step by step visual. sorry for the inconvenience, i wish there was more i could show you, but that's what i need help with

Answer 6

to explain why i got those answers

Answer 7

after this try sin(2pi/3)

just to see how will change the result

Answer 8

after sin(4pi/3)

and at the last one try the sin(5pi/3)

Answer 9

sin(pi/3) is in quadrant one

sin(2pi/3) is in second quadrant

sin(4pi/3) in 3rd quadrant

sin(5pi/3) in 4th quadrant

Answer 10

ohh ok

Answer 11

sin pi/3 is sin60 degree = sqrt3 /2

Answer 12

in fuction of these quadrants just changing the sign of plus on minus

Answer 13

Actually, it's the angle pi/3 that is in quadrant I. We want to find the sine of this angle.
Starting with the positive x-axis, which represents an angle of zero, pivot around the origin counterclockwise to pi/3 (equivalent to 60 degrees). Draw a ray from the origin to that circle shown on your drawing.

Draw a straight line from that point on the circle straight down to the positive x-axis.
That line represents the side "opposite" the angle.

Darken the line segment on the positive x-axis from the origin to the point where the "opposite side" intersects the positive x-axis. This is the side "adjacent to" the angle.


If you have a chart of the unit circle, you may be able to read off the lengths of the "opp side" and the "adj side." They are Sqrt(3) and 1 respectively.

The Pythagorean Theorem will give you the length of the ray you drew at the beginning:

Since x^2+y^2=r^2,
\[1^2+(\sqrt{3})^2=2^2, so~the~radius ~is ~r=2.\]

Answer 14

The sine of pi/3 is thus opp/hyp = Sqrt(3) / 2.

Actually, once you've worked with trig functions a while, you'll probably remember this fact easily and not have to go through all these steps to find sin pi/3.