Do Now• Take your calculator from the front.• Put your work from the gallery walk in class

yesterday on your desk with the score on top ready to be stamped. (Add your total if you haven’t already.)

• Sit in your seating chart and assign roles to your group members:– Team captain– Materials gatherer– Scorekeeper– Spokesperson

Announcements

• Test tomorrow/Friday• When you start the test, turn in:

– Notebook for notebook check (fold over any pages with stamps)

– Vocab from yesterday– Quiz corrections

PYTHAGOREAN

THEOREM

© 2006 by Mr. Mayers

TRIGONOMETRYDISTANCE

UNIT CIRCLE TRIG IDENITITIES PROVE IT!

Team 1 Team 2 Team 3 Team 4

0 0 0 0

What is the Pythagorean Theorem and when does it

work?

Back

a2 + b2 = c2,

Finding missing sides of right triangles

Which trig ratio is represented by opposite leg/adjacent leg?

Back

tangent

What is the distance between (1, 2) and (4, 6)?

Back

5

Why is the unit circle called the unit circle?

Back

Because the radius is 1 unit

Back

Take the cosine of the reference angle

How do you find the x-coordinate of a point around

the unit circle?

Back

What could the following picture be used for?

Proving the Pythagorean Theorem

A right triangle has a leg of length 7cm and a hypotenuse of length 25cm. What is the length of the missing leg?

Back

24cm

Which method could be used to solve the following problem?

BackCosine/30-60-90 triangle

What is the distance formula?

Back

Back

Identify the center and the radius of the unit circle.

Center: (0, 0), Radius: 1

Back

x= 7.44cm

Solve for x.

Back

Solve for a. What property did you use?

a=127, line has 180o

Do the following side lengths form a right triangle? Why/why not?

4, 8, 9

Back

No, a2 + b2 ≠ c2 .

Solve for a.

Back

a=5

What is the distance between (-2,3) and

(6,1)?

Back

8.2

Back

What are the coordinates of a point on the unit circle 59o from the initial position?

(.5150, .8572)

Back

What does tangent represent in the unit circle?

Slope. Sin/cos.

Back

If I have two straws, lengths 6inches and 5inches, what possible other lengths of

straws could make a triangle?

Back7.94

Find the missing side length

List the trig ratios and their meanings. Include the

acronym.

Back

Sine=opposite/hypotenuse, cosine=adjacent/hypotenuse,

tangent=opposite/adjacent

Back

52.4

What is the perimeter of ABC with vertices A(3,5), B(9,13), and C(25,1)

Back

What is the maximum angle measure around the unit circle?

There is no maximum. It’s unlimited

Back

Find the area of the shape.

Back

Prove the Pythagorean Theorem

Find the area.

Back

A=49.7

(missing side is 3.7)

Solve for the missing angle.

Back

36.87o

How is the distance formula related to the Pythagorean Theorem?

Back

x2-x1 represents a leg…

Back

(-1,0)

What are the coordinates of the point 180o from the initial position? 

Back

What is the Pythagorean identity? How is it related to the Pythagorean Theorem?

Sin2 + cos2 =1

Back

½ (a+b) (a+b) = ½ ab + ½ ab + ½ c2

Find the area of the figure in two different ways. Hint: It can be a

trapezoid or it can be three triangles.