4.2 The Unit Circle! Whoa wait a sec, where does all that stuff come from?

1. 4.2 The Unit Circle! Whoa wait a sec, where does all that stuff come from?

2. Let's go on a unit circle adventure and find out! Since our special right triangles (or commonly used triangles are 30-60-90 and 45-45-90, let's split our circle into increments of 30 (12ths of the circle) and 45 (eights of the circle).

3. Convert degrees to radians

4. eights of full circle, fourths of half circle fourths of full circle, halfs of half circle think 45/360 = 1/8 think 90/360 = 1/4

5. twelfths of full circle, sixths of half circle think 30/360 = 1/12

6. Mind Blown

7. Review! What if the hypotenuse was 1? SOHCAHTOA Special Right Triangles

9. Let's talk special right triangles With a hypotenuse of 1, find the missing side lengths using the Pyth. thm. 45-45-90 Triangle l 45 1 45 x 2 45 x 45 x Find sin(45)= cos(45)= tan(45)=

10. Let's talk special right triangles With a hypotenuse of 1, find the missing side lengths using the Pythagorean thm. hint: think of an equilateral triangle 30-60-90 Triangle 1 60 2x 60 x 30 30 x 3 Find sin(30)= cos(30)= tan(30)= Find sin(60)= cos(60)= tan(60)=

11. Now we can find the coordinates of each point on the circle Remember the hypotenuse is 1! 60 30 45 1 y 30 45 x 60 cos(45) = x/1 x = cos(45) x = sin(45) = y/1 y = sin(45) y = cos(30) = x/1 x = cos(30) x = sin(30) = y/1 y = sin(30) y =

12. 2 (mind blown)