Section 2.2 – Basic Trigonometric Values

(0, 1) (1,0) (-1, 0) (0, -1)

Summary of Denominators of 2

30 60 1 2 60 30 1 2 45 1

30 60 1 60 30 1 45 1

Summary of Denominators of 2

Summary of Denominators of 3

Denominators of 3 Denominators of 6 Denominators of 4

ALMOST 1 (-, +) NUMERATOR 1 (+, +) JUST PAST 1 (-, -) ALMOST 2 (+, -)

Denominators of 3 Denominators of 6 Denominators of 4

Numerator 1 (+, +) Almost 2 (+, -) 2 1 Almost 1 (-, +) Past 1 (-, -)

+ + + _ _

Let’s try a few more examples….. Num 1 (+, +) 3 = 1 + 2 Past 1 (-, -) 4 = 2 x 2 Almost 2 (+, -) 6 = 3 x 2 Almost 1 (-, +) 3 = 1 + 2 Make Negative Make Negative Past 1 (-, -) 3 = 1 + 2 Make Negative

Redefine the wrapping function values Instead of we will now think of the wrapping function as

WE KNOW THEREFORE

Now it’s your turn. To find each trig value: Find the wrapping function value Choose the appropriate coordinate

We can’t forget the negatives either……here we go: So when dealing with negative ‘arclengths’ The value of the cosine (cos) remains unchanged The value of the sine (sin) will change Now try these three……

First a little arithmetic review:

We define and

We define and