TRIGONOMETRY {Trig Identities}

TRIGONOMETRY  {Trig Identities}

The sine, cosine and area rules are introduced in grade 11, as well as problems in two dimensions.

The identities:                Remember

tan²θ = sin² θ/cos² θ        sin A = opp / hyp   = a / c

sin²θ+cos²θ = 1              cos A = adj / hyp  = b / c

                                        sin² A   +   cos ² A

                                        =  (a/c) ²   +  ( b/c)²

1.   Simplify:

(a)       sin(180⁰ +A)

cos(180⁰ - A)

       (b)         cos (90⁰ + A)               .

    tan(180⁰ – A).cos( 360⁰+A)

2.     Prove the following identities:

      (a)         8              4         =       4       

Sin²A    1+cos A        1-cos A

                   

      (b)         cos²A           1       +     1            =    – 2 sin A             

                                          sinA -1)     sinA +1)

   

3.      Given that cos 58°= k, find the following in terms of k, without

         using a calculator:

(a)     sin 212°

(b)tan(-58°)

(c)      sin 148°

Joseph Louis Lagrange

"Before we take to sea we walk on land, before we create we must understand.”

Joseph Lagrange French born mathematician first put his feet on Italian soil. He mostly dealt with calculus an area in mathematics and he impressed a lot of people with his knowledge on this subject. Mr. Lagrange the director of mathematics in November 1766 took this post over by other mathematician Euler.

His interest in mathematics started in 1693 when he read a copy of Halley’s work on the use of algebra. Joseph was not only attracted to maths but also to physics where by the excellent teaching of Baccaria at college of Turin and where he made a decision to make mathematics a career.

Joseph made a discovery in 1754 a very important discovery that contributed substantially to the subject calculus of variations. The discovery made by Joseph was about the tautochrome. The mathematicians started to study this but did not receive the name calculus of variations, where Euler called it in 1766.

When Joseph made this discovery he send Euler his results on the tautochrome where it contained the methods he used. Euler received the letter and replied on the 6 of September where he was impressed by Joseph who was only 19 years of age, were appointed to professor of mathematics at the Royal Artillery School in Turin on September 1755. The young boy deserved this and he showed the world of mathematics that there is great talent in the originality of in death thinking.

Years later “Napoleon named Lagrange to the Legion of Honour and Count of the Empire in 1808. On 3 April 1813 he was awarded the Grand Croix of the Ordre Impérial de la Réunion and he died a week later.”

This shows us as students and scholars that age is nothing but a number and that the knowledge we have, we can use and discover great things.

"When we ask advice, we are usually looking for an accomplice."

Sums, numbers, and mathematical eqautions not  your favourite thing or subject in the world come take a trip with me the Mathstudent and enjoy the adventure. Maths? Why maths you ask your self frequently? Well follow me  I’ll take you places.

The theme of my blog is a mathematical  and science  template which describes mostly what the blog is about. If you look at the color scheme of the theme you’ll see that it is black (dark background) where scholars mostly would find themselves in when they in a difficult situations. The same apply to the word math’s the subject of hell as they describe it in some of the schools I’ve been to.

The reason most of the kids today describe the subject as hell is because they don’t understand the work they are doing or they don’t do any of the homework given to them by their teacher and when they don’t pass they want to put the blame on the teachers but do the parents go through their children’s books daily just to take note of what is happening in their child’s life or schoolwork?

  The numbers and the equations (the colour white) on my theme is there to help you think deeper and assist you so that you can see even though you trapped in a dark place there’s always light at the end of the tunnel to make things easier for you.

You can accomplish the things in life that is difficult by not taking the easy route that’s by leaving the math’s but by taking the hard route which is to work hard. 

Mathematics can also be a description for discipline because it is an organised study field where you define different types of problems that you have to address. There are also methods to use to address to solve the problems.

Maths is also a disciplinary tool. As the language subjects where reading, writing etc is important the same apply to maths where you the doing and the understanding is more of the importance of the day basically the learning of maths.

Mathematics as a discipline is thus so that you must work harder and do more work than just the work you get by the teacher in your class. The more you practice the maths sums etc the better the understanding would be of the things.

about myself

I am Thagan Deal, a student at CPUT Wellington, a teacher in the future for your children. Yes you read it. i'm currently studying B.ed FET fase at the CPUT astablished in wellington. I'm an out going person and like having fun in my free time and spending time with my friends. I am also into sports different kinds of sports actuly but my favorite sport is rugby. Rugby is the first sport i played since i started my school carreer and i enjoyed it the first time I played it. I am a proud STORMER suporter.