Mates y TIC - Maths and ICT

Actividades de Matemáticas con TIC - Math Activities with ICT - - - (matesytic@gmail.com) Ricardo García Mesa

Archive for January, 2019

Moving Homer with vectors

Posted by ricardogm on 31st January 2019

Hi

We are going to use vectors to create animations, similar to this applet:

Pay attention and send me the files, as usual.

The math thing we are going to use is “linear combinations of vectors“, which is simply a·u+b·v, being  u and v vectors and a and b, numbers.

1. First, an easier construction. We are going to generate something similar to this:

2. Now, the Homer thing. It’s more difficult, so you have to pay even more attention than usual Wink.

The images you need are in this folder:

Images

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Problemas de optimización resueltos

Posted by ricardogm on 29th January 2019

Pues eso:

Problemas

Pasos para la resolución de problemas de optimización:

1  Se plantea la función que hay que maximizar o minimizar.

2  Se plantea una ecuación que relacione las distintas variables del problema, en el caso de que haya más de una variable.

3  Se despeja una variable de la ecuación y se sustituye en la función de modo que nos quede una sola variable.

4  Se deriva la función y se iguala a cero, para hallar los máximos-mínimos locales.

5  Se realiza la 2ª derivada para comprobar el resultado obtenido o, alternativamente, se comprueba el valor de la función en los máximos-mínimos y en los extremos de su dominio.

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Vectors

Posted by ricardogm on 28th January 2019

Basic things:

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Trigonometric ratios in every quadrant

Posted by ricardogm on 28th January 2019

Hi

We have seen this thing before:

Now we are going to work with it a little more. Go to this page.

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Trigonometric identities and homer measuring trees

Posted by ricardogm on 21st January 2019

 Hi

We are going to prove these two famous trigonometic identities:

sin2(x) + cos2(x) = 1

tan(x)=cos(x)/sin(x)

that can be seen in this applet:​

And how to measure trees with trigonometry (we are going to do more or less the same thing):

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Goniometric circumference

Posted by ricardogm on 18th January 2019

 

Hi

Today we are going to create something similar to this:

The idea is to study the trigonometric ratios of angles greater than 90º.

Pay attention. Send me the file.

Now time to solve some problems in your notebook:

trigonometry-word-problems.pdf

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Soluciones temas 13 y 14

Posted by ricardogm on 18th January 2019

 

Pues eso:

Tema 13

Tema 14

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3-gonometry-2

Posted by ricardogm on 10th January 2019

Hi

We have some things to do:

0. Solve these problems in your notebook while I try to correct your homework. Make drawings, of course.

1 The known data for a right triangle ABC is a = 5 m and B = 41.7°. Solve the triangle.

2 The known data for a right triangle ABC is b = 3 m and B = 54.6°. Solve the triangle.

3 The known data for a right triangle ABC is a = 6 m and b = 4 m. Solve the triangle.

4 The known data for a right triangle ABC is b = 3 m and c = 5 m. Solve the triangle.

5 A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time.

6 An airship is flying at an altitude of 800 m when it spots a village in the distance with a depression angle of 12°. How far is the village from where the plane is flying over?

7 Find the radius of a circle knowing that a chord of 24.6 m has a corresponding arc of 70°.

8 Calculate the area of a triangular field, knowing that two of its sides measure 80 m and 130 m and between them is an angle of 70°.

9 Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of 30º and from 10 m closer the top can be seen at an angle of 60°.

10 The length of the side of a regular octagon is 12 m. Find the radii of the inscribed and circumscribed circles.

11 Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of 49 centimeters.

12 Three towns A, B and C are connected by roads which form a triangle. The distance from A to C is 6 km and from B to C, 9 km. The angle between these roads is 120°. How far are the towns A and B from each other?

And here you have the solutions..

2. More problems.

The drawing below shows nicely what we are going to do:

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