Trignometry

1. y=x + 3, y=x² + 6x + 9, y= x-3

Solution: x= -3, y=0 or x=-2, y=1

y= x+3= x² + 6x + 9

            x+3= x² + 6x + 9

            0= x²+ 5x + 6

            Solving by factorization

            a+b=5

            aXb= 6

            x²+ 2x+ 3x + 6

            0=x(x+2) + 3(x=2)

            0=(x+3)(x+2)

x= -3, y= 0

x= -2, y= 0

• y= -x – 4, y=-x+2, y=x-3

y= -x – 4

X	-4	-3	-2	-1	0	1	2	3	4	5
y	1	0	-1	-2	-3	-4	-5	-6	-7	-8

y= -x+2

X	-4	-3	-2	-1	0	1	2	3	4	5
y	6	5	4	3	2	1	0	-1	-2	-3

y= x-3

X	-4	-3	-2	-1	0	1	2	3	4	5
y	-7	-6	-5	-4	-3	-2	-1	0	1	2

Solution: x=2.5 y= -0.5 or x= 0.5, y= -3.5

• 2x + -5y = 10

            -5y = -2x -10

            y = 0.4x + 2

X	-5	-4	-3	-2	-1	0	1	2	3	4	5
y	0	0.4	0.8	1.2	1.6	2	2.4	2.8	3.2	3.6	4

Solution=  y=2, x=-5

• 2x – 4y=9

-4y= 9-2x

y=-2.25+0.5x

X	-4	-3	-2	-1	0	1	2	3	4	5
y	-4.25	-3.75	-3.25	-2.75	-2.25	-1.75	-1.25	-0.75	-0.25	0.25

Solution = y= -2.25, x= 4.5

• y=3, x=4

Solution (x,y) = (4,3)

• y= √ x-4, y= √ x+3

= (y)²= (√ x-4 )²

⁼ y² = x-4

 X= y² +4

y	-4	-3	-2	-1	0	1	2	3	4	5
Y2	16	9	4	1	0	1	4	9	16	25
4	4	4	4	4	4	4	4	4	4	4
x	20	13	8	5	4	5	8	13	20	29

Y= √ x+3

            (y)²= (√ x+3)²

                Y²=x + 3

            X=y² – 3

y	-4	-3	-2	-1	0	1	2	3	4	5
Y2	16	9	4	1	0	1	2	9	16	25
-3	-3	-3	-3	-3	-3	-3	-3	-3	-3	-3
x	13	6	1	-2	-3	-2	1	6	13	22

• y=x^2, y=x²+ 3, y= x² – 4

y=x²

X	-4	-3	-2	-1	0	1	2	3	4
y	16	9	4	1	0	1	4	9	16

y=x²+ 3

X	-4	-3	-2	-1	0	1	2	3	4
X2	16	9	4	1	0	1	4	9	16
3	3	3	3	3	3	3	3	3	3
y	19	12	7	4	3	4	7	12	19

y= x² +- 4

X	-4	-3	-2	-1	0	1	2	3	4
X2	16	9	4	1	0	1	4	9	16
-4	-4-	-4	-4	-4	-4	-4	-4	-4	-4
y	12	5	0	-3	-4	-3	-3	0	5

• Difference between -√ (3) and √ (-3)

          -√ (3)= -1.73205

          √ (-3)= Impossible

• y= 3x² – 2 between 5,5

          when x= 5, y= 3(5²)-2

                             =3(25)-2

                              =73

                      When y= 5, 5= 3x² -2

                                          3x²=5+2

                                          3x²= 7

                                          X² =7/3

                                         X= √7/3

1. y= √x+5, Between {-10,10}

          when x =-10

                    y²=x+5

                    y²= -10 +5

                    y²= -5

                    √y²=√-5: Impossible to acquire a root of a negative number because there is no a negative square.

          When y= 10

                    10²= x +5

                     100= x+5

                     X=95

1. y=/x+5/ between {-15,5}

          when x= -15

                    y= x+5

                        = -15+5

                    Y= -10

          When y= 5

                   5=x-5

                    X= 5+5= 10

1. y=/x-5/ between {10, -5)

          when x=10

                    y= 10-5

                        = 5

          When y= -5

                    -5= x-5

                                 X=0

1. 3x + y = 10

          Y= 10-3x

X	-5	-4	-3	-2	-1	0	1	2	3	4	5
y	25	22	19	16	13	10	7	4	1	-2	-5

Solution= when x=0, y= 10 and when y=0, x =3.3

1. (x²– 2xy – y²) (x²+2xy+y²)

Opening the brackets and putting like terms together

x²(x²+2xy+y²) = x⁴ +2x³y+x²y²

– 2xy (x²+2xy+y²) = -2x³y- 2x²y² -2xy³

– y² (x²+2xy+y²) = x²y² +2xy³ + y⁴

Therefore, solution = x⁴ +y⁴

15.

1. (x- y) (x²+xy + y²)

        Opening the brackets

            x(x²+xy + y²) -y(x²+xy + y²)

            x³ +x²y + xy² -x²y- xy²-y³

        Putting like terms together

            x³ +(x²y -x²y) + (xy² – xy²)-y³

Therefore solution= x³ -y³

1. (x+ y) (x²+xy + y²)

        Opening the brackets

            x(x²+xy + y²) +y(x²+xy + y²)

            x³ +x²y + xy² +x²y+xy²+y³

        Putting like terms together

            x³ +(x²y +x²y) + (xy² +xy²)+y³

        Therefore solution= x³ +2 x²y + 2 xy² +y³

1. (x- y) (x²-xy + y²)

        Opening the brackets

            x(x²-xy + y²) -y(x²+xy + y²)

            x³ -x²y + xy² -x²y-xy²-y³

        Putting like terms together

            x³ -(x²y -x²y) + (xy² -xy²)+y³

        Therefore solution= x³ -2 x²y + y³

1. (x+y) (x²– xy + y²)

        Opening the brackets

            x(x²-xy + y²) +y(x²-xy + y²)

            x³ -x²y + xy² +x²y-xy²+y³

        Putting like terms together

             x³ -(x²y +x²y) + (xy² -xy²)+y³

        Therefore solution= x³ +y³