Help with Unit Circles!

firemath

firemath

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Oct 29, 2019
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I am having so much trouble understanding these. Could someone give me a clear explanation?
 
a circle of radius one centered at the origin.

what don't you understand?
 
Unit circle? It is a circle with r =1 unit.
If the center of this unit circle is (a,b), then the equation of the circle would be (x-a)^2 + (x-b)^2 = 1
 
So my professor is having us solve trig ratios with them. I don't really understand how to to do this when the angle is given in terms of, say, pi/6.
 
I have taught trigonometry countless times and never talked about the unit circle as you are talking about.
You can get away from using the unit circles if you know the following.
1) The graph of the sin(x) and cos(x) to find out the sin(x) and cos(x) values when x = 0, pi/2, pi, 3pi/2 and 2pi
2) Know the the special triangles 30-60-90 and 45-45-90.
This will give you exactly what the unit circle will give you.

In the future please ask clearer questions.
 
What are the exact values of the following trigonometric functions?

  1. cos495∘
  2. tan5π3
Use the unit circle and show your work.
 
what they are really after here is making sure you get the signs of the various functions correct.

do you understand about the 4 quadrants of the unit circle?
 
Romsek said:
what they are really after here is making sure you get the signs of the various functions correct.

do you understand about the 4 quadrants of the unit circle?
Click to expand...

Yes. I understand the composition of the unit circle.
 
ok so the idea is mod your angle with 2 pi (360 deg) and figure out what quadrant it lies in.
Then put a point on the unit circle at that angular value.

then the signs of the trig functions vary by quadrant as

I - all positive
II - cos, tan are negative
III - sin, cos are negative
IV - sin, tan are negative

you can see this by dropping vertical and horizontal lines to the axes from your point on the unit circle and seeing what sign they correspond to.
 
Romsek said:
ok so the idea is mod your angle with 2 pi (360 deg) and figure out what quadrant it lies in.
Then put a point on the unit circle at that angular value.

then the signs of the trig functions vary by quadrant as

I - all positive
II - cos, tan are negative
III - sin, cos are negative
IV - sin, tan are negative

you can see this by dropping vertical and horizontal lines to the axes from your point on the unit circle and seeing what sign they correspond to.
Click to expand...
Thank you!
 
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