1. M3U7D2 Warm Up (x+4)2 (x-7)2 c = 36 (x+6)2 1. Factor 2. Factor
What would the value of c that makes
a perfect square. Then write as a perfect square.
(x+4)2
(x-7)2
c = 36
(x+6)2

2. HW Check Document Camera

3. U7D2 Unit Circle
OBJ: Build an understanding of trig functions by using tables, graphs and technology to represent the cosine and sine functions.
Interpret the sine function as the relationship between the radian measure and an angle formed by the horizontal axis and a terminal ray on the unit circle and its y coordinate.
Interpret the cosine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its x coordinate.

4. WRITE THIS DOWN on pp. 7
The Unit Circle
Definition: A circle centered at the origin with a radius of exactly one unit. Let’s develop!
(0, 1)
| |
(-1,0)
(0 , 0)
(1,0)
(0, -1) 4

5. What are the angle measurements of each of the four angles we just found?
π/2
90° 0° 2π
180°
360° π
270°
3π/2 5

6. The Unit Circle WATCH Let’s look at an example
In order to determine the sine and cosine we need a right triangle.
The x-coordinate of this has a value of the cosine of the angle. The y-coordinate has a value of the sine of the angle. 1 30 -1 1 -1

7. WATCH
The Unit Circle
Create a right triangle, using the following rules:
The radius of the circle is the hypotenuse.
One leg of the triangle MUST be on the x axis.
The second leg is parallel to the y axis. 1 30 -1 1 -1 60 2 1
Remember the ratios of a triangle- 30

8. The Unit Circle WATCH 2 60 1 1 30 P X- coordinate 30 -1 1P
X- coordinate 30 -1 1
Y- coordinate -1

9. Angles and the Unit Circle
WATCH
Find the cosine and sine of 135°.
From the figure, the x-coordinate of point A 
is – , so cos 135° = – ,or about –0.71. 2
Use a 45°-45°-90° triangle to find sin 135°.
opposite leg = adjacent leg
0.71   Simplify.
=    Substitute. 2
The coordinates of the point at which the terminal side of a 135° angle intersects are about (–0.71, 0.71), so cos 135° –0.71 and sin 135°

10. Angles and the Unit Circle
WATCH
Find the exact values of cos (–150°) and sin (–150°).
Step 1:  Sketch an angle of –150° in standard position. Sketch a unit circle.
x-coordinate = cos (–150°)
y-coordinate = sin (–150°)
Step 2:  Sketch a right triangle. Place the hypotenuse on the terminal side of the angle. Place one leg on the x-axis. (The other leg will be parallel to the y-axis.)

11. Angles and the Unit Circle
WATCH
(continued)
The triangle contains angles of 30°, 60°, and 90°.
Step 3: Find the length of each side of the triangle.
hypotenuse = 1 The hypotenuse is a radius of the unit circle.
shorter leg = The shorter leg is half the hypotenuse. 1 2 1 2 3
longer leg = ∙ = The longer leg is 3 times the shorter leg. 3 2 1
Since the point lies in Quadrant III, both coordinates are negative. The longer leg lies along the x-axis, so
cos (–150°) = – , and sin (–150°) = – .

12. THEREFORE: The Unit Circle
WRITE THIS DOWN
THEREFORE: The Unit Circle
A circle with radius of 1 has the
Equation x2 + y2 = 1

13. Switch to document Camera
Develop Unit Circle Measures
Demonstrate how to find angle measure in radians in Quadrant I
Expand to all four quadrants
Demonstrate how to find since and cosine

14. The Unit Circle with Radian Measures
COMPLETE ON HANDOUT
The Unit Circle with Radian Measures

15. SOH CAH TOA Sine is Opp/Hyp Cosine is Adj/Hyp Tangent is Opp/Adj
FYI…M2 REMINDERS ???
SOH CAH TOA
Sine is Opp/Hyp
Cosine is Adj/Hyp
Tangent is Opp/Adj
Cosecant is 1/Sine
Secant is 1/Cosine
Cotangent is 1/Tangent

16. SOH CAH TOA

17. Test Corrections due Thursday 5/3/18
Classwork
Test Corrections due Thursday 5/3/18
pp. 8
Homework
pp. 9&10
AND complete the unit circle games (QUIZ) on the next slide– me a screenshot of your score by FRIDAY 5/11/18!

18. Study Aids Terminal Side Coterminal Unit Circle Song
Degrees to radians flashcards
Degrees, Radians and Coordinate points flashcards
Angles of the Unit Circle – Radians QUIZ
Angles of the Unit Circle - Degrees QUIZ