Razones Trigonometricas

1. TRIGONOMETRIA
SISTEMA DE MEDICION DE ANGULOS
Ciclo 5

2. SISTEMA DE MEDICION DE ANGULOS
QUE ES UN ANGULO?
1. Porción de un plano limitado por dos líneas que parten de un mismo punto
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3. EXPLICACION

5. MEET THE
TEACHER
Images reveal large amounts of
data, so remember: use an image
instead of a long text. Your
audience will appreciate it

6. TABLE OF CONTENTS
01
FUNCTIONS
You can describe the
topic of the section
here
02
DEGREES
You can describe the
topic of the section
here
03
GRAPHICS
You can describe the
topic of the section
here

7. Here you can give a brief description of the topic
you want to talk about. For example, if you want
to talk about Mercury, you can say that it’s the
smallest planet in the entire Solar System
INTRODUCTION
TO POLYNOMIALS

8. 01
POLYNOMIAL
FUNCTIONS
You can enter a subtitle
here if you need it

9. Do you know what helps you make your point
clear? Lists like this one:
● They’re simple
● You can organize your ideas clearly
● You’ll never forget to buy milk!
And the most important thing: the audience
won’t miss the point of your presentation
ABOUT POLYNOMIAL
EXPRESSIONS

10. ADDING AND SUBTRACTING
POLYNOMIALS
ADDITION
Mercury is the closest planet
to the Sun and the smallest
one in the Solar System
SUBTRACTION
Venus has a beautiful name
and is the second planet
from the Sun

11. MONOMIAL
BINOMIAL
Despite being red, Mars is
actually a cold place
SHORTCUT
A
B Saturn is a gas giant and the
biggest in the Solar System
C Mercury the closest planet to
the Sun and the smallest one
MULTIPLYING MONOMIALS
AND BINOMIALS

12. COMBINE
Despite being red, Mars is
actually a cold place
Mercury is the closest
planet to the Sun
MULTIPLY
DISTRIBUTE
01
02
03 Venus is the second
planet from the Sun
04
RESULT
Jupiter is the biggest
planet in the Solar System
MULTIPLYING POLYNOMIALS

13. HOW TO MULTIPLY TWO
BINOMIALS: FOIL
FIRSTS
Venus is the
second planet
INNERS
Mercury is the
smallest planet
LASTS
Mars is a very
cold place
OUTERS
Neptune is very
far from the Sun
a-c b-d
b-c
a-d
(a+b)(c+d)

14. ABOUT POLYNOMIAL TERMS
MONOMIAL
Mercury is the closest
planet to the Sun and
the smallest one
BINOMIAL
Mars is full of iron
oxide dust, which gives
the planet its red cast
TRINOMIAL
Jupiter is a gas giant
and the biggest planet
in the Solar System
1 TERM 2 TERM 3 TERM
3x 2x + 7 5x - 2y + 4z

15. Saturn is composed
mostly of hydrogen
VARIABLE
FUNCTIONS
Jupiter is the biggest
planet of them all
MATRIX
Despite being red,
Mars is a cold place
GRAPHS
COEFFICIENT CALCULUS
Mercury is the
smallest planet
Venus is the second
planet from the Sun
Neptune is very far
from the Sun
REVIEWING CONCEPTS IS
A GOOD IDEA

16. AWESOME
WORDS

17. A PICTURE IS
WORTH A
THOUSAND
WORDS

18. 02
POLYNOMIAL
DEGREES
You can enter a subtitle
here if you need it

19. DEGREE OF A POLYNOMIAL
DEGREE POLYNOMIAL DESCRIPTION
0 9 It's the fourth-brightest object
1 x¹ + 4 It's composed of hydrogen
2 x² + x¹ + 5 It's also the fourth-largest object
3 2x³ + 11x² Mercury is the closest planet
5 x²y5 + 6x⁴ + y¹ Neptune is the farthest planet

20. THIS IS A GRAPH
JUPITER
Jupiter is the
biggest planet
x = 0
NEPTUNE
Neptune is very
far from the Sun
y = 0
Follow the link in the graph to modify its
data and then paste the new one here.
For more info, click here
MERCURY
Mercury is the
smallest planet
x = 2
MARS
Mars is actually a
very cold place
y = 2

21. x² + x¹ + 5
Saturn is a gas giant and
has several rings
x¹ + 4
Jupiter is a gas giant and
the biggest planet
2x³ + 11x²
Neptune is the farthest
planet from the Sun

22. 5x² x 2y - 7
Examples of polynomials catch your audience's attention

23. 40% 80%
POLYNOMIAL PERCENTAGES
MERCURY
It’s the closest planet to the
Sun and the smallest one
VENUS
Venus has a beautiful name
and is the second planet

24. THIS IS A MATH MAP
JUPITER
Jupiter is a gas giant
and the biggest planet
32.000
NEPTUNE
Neptune is the farthest
planet from the Sun
25.600

25. Saturn is composed
mostly of hydrogen
MULTIPLY
CHECK
Jupiter is the biggest
planet of them all
ADD
Despite being red, Mars
is a cold place
FACTORS
VALUES
Mercury is the closest
planet to the Sun
Saturn is the farthest
planet from the Sun
C
A
D
B
E
FACTORING TRINOMIALS

26. FACTORING POLYNOMIALS:
GREATEST COMMON FACTOR
FIND GCF
Venus is the second
planet to the Sun
FACTOR
Neptune is the farthest
planet from the Sun
PRODUCT
Jupiter is a gas giant
and the biggest planet
STEP 1 STEP 2 STEP 3

27. FACTORING TECHNIQUES
2yx² - 8xy - 24y
= 2y (x² - 4x - 12)
FACTOR THE GCF
SPECIAL CASES GROUPING
4x² - 4x - 15
= 4x² - 10x + 6x 15
= 2x (2x - 5) + 3 (2x - 5)
= (2x + 3) (2x - 5)
x² - 9
= x² - 3²
= (x + 3) (x - 3)
Difference of
two squares
x² - 10x +25
= (x - 5)²
Perfect square
trinomial

28. FACTORING POLYNOMIALS:
DOUBLE GROUPING
EXAMPLE 1
2x² + 8x + 3x + 12
First grouping Second grouping
(2x² + 8x) (3x + 12)
2x (x + 4) + 3 (x + 4) = (x + 4) (2x + 3)
EXAMPLE 2
3x² + 6x + 4x + 8
First grouping Second grouping
(3x² + 6x) (4x + 8)
3x (x + 2) + 4 (x + 2)

29. FACTORING POLYNOMIALS
COMPLETELY
● Venus has a beautiful name and
is the second planet to the Sun
● It’s terribly hot, even hotter than
Mercury, and its atmosphere is
extremely poisonous
● It’s the second-brightest natural
object in the night sky
● Mercury is the closest planet to
the Sun and the smallest one in
the Solar System
● This planet's name has nothing
to do with the liquid metal
● Mercury was named after the
Roman messenger god
PROBLEM SOLUTION

30. WHAT IS THE DIFFERENCE
A polynomial function would be...
A polynomial expression is just...
A polynomial equation is...
01
03
02
y = f(x) = x² - 3x + 2
x² - 3x + 2
x² - 3x + 2 = 0

31. TRY IT: WHAT IS THE PRODUCT?
(4y - 3)(2y² x 3y - 5)
8y³ + 3y + 15
8y³ - 23y + 15
8y³ + 6y² + 17y + 15
8y³ + 6y² + 29y + 15
Mercury is the closest planet to the Sun and the
smallest one in the Solar System. This planet's name
has nothing to do with the liquid metal

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