Unit circle (math)?

Question

In math class, I am currently learning about Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent. We have also just started a lesson on the unit circle. I have all the coordinates for the Unit Circle all plotted out for 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, and 360 degrees.

How do I find the Sin of 30 degrees? How do I find the Cosine of 30 degrees? How do I find the tangent of 30 degrees? The points for 30 degrees are, (square root of 3 divided by 2, 1/2).

Here is a link to the unit circle that I found on the internet:
http://hrsbstaff.ednet.ns.ca/eplee/images/Unit%20Circle.jpg

Answer 1

Oh my God! I can only hope the best for you because that mathematical question is very complex!! Good luck!

Answer 2

The sine is the y-axis, and the cosine is the x-axis. So:

sin 30 = 0.5
cos 30 = Sqrt[3]/ 2

The tangent is equivalent (always equal to), the sine divided by the cosine

i.e. tan 30 = sin 30 / cos 30

You know what sin 30 and cos 30 is from the unit circle, so you can evaluate it as follows:

tan 30 = 1/ Sqrt[ 3 ]

Answer 3

you commit to memory the dimensions of the following two triangles

1) a right-angled triangle, height 1/2
hypot. 1
length: work it out using pythag

(this figure is really half an equilateral triangle with side 1)

the angles it contains are 30, 60 and 90 degrees

2) a right-angled isosceles triangle with both legs 1

hypot: sq.rt 2

the angle it contains are 45 and 90 degrees

then in 1)

sin 30 = 0.5
cos 30 = 0.866
sin 60 = 0.866
cos 60 = 0.5

in 2) sin 45 = cos 45 = 0.707 (or 1/sq.rt 2)

this mnemonic is found in plato's Timaeus

Answer 4

On the unit circle, sine = the y coordinate.
So sin (30)=sin(Pi/6)=1/2

The cosine = the x coordinate
So cos(30)=cos(Pi/6)=sqrt(3)/2

The tangent = y/x
So tan(30)=tan(Pi/6)=1/sqrt(3)