Unit Circle

Why do you think this is called a "unit circle"?

• Because it has units on it

• Because it has radius of 1 unit

• Because it lives in a single-unit condo

The highlighted coordinate to the left  of the circle is (-1, 0) because

• the vertical distance is 1  and the horizontal distance is 0 

• the horizontal distance is 1 to the right and the vertical distance is 0 

• the horizontal distance is 1 to the left and the vertical distance is 0 

• it is binary code

You can get these values for x and y using  . . .

• Pythagorean's theorem

• Inverse trigonometry

• Special right triangle rules

What is the measure of the reference angle going to be?

• 150

• 30

• 180

How did  he get   for the horizontal leg of the triangle

• The hypotenuse is 1

  The short side is 1/2  or half the hypotenuse

  The long side is the short side times   which gives us 

• The hypotenuse is 1/2

  The short side is 1, or twice the hypotenuse

  The long side is the short side times   which gives us  

• The long side should not be   

Why negative?

• Because it is glass half empty

• Because the coordinate is to the left and left is the negative direction for x

• Because we subtracted 1

So it looks like .. . 

• cosine is the x coordinate and sine is the y coordinate

• sine is the x coordinate and cosine is the y coordinate

• sine and cosine are the same value

What is the cosine of 90 degrees?

• 0

• 1

What is the sin of 90 degrees

• 0

• 1

This is called . . . .

• squaring the denominator

• rationalizing the denominator

• multiplying by the reciprocal