Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Trigonometry

Hi
Why cos (3x)×cos (3x) does not equal to cos (9x2)
Whay we cannot multiple it
Why we write cos square (3x)??

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

hi Zeeshan 01

You can always put in a value for x and test this for yourself.  If the numbers do not agree then the algebra is wrong.

Let us examine what you have there.  Two separate functions: first times x by 3 and second find the cosine of the result.

You cannot multiply together cos(3x) with another cos(3x) to make cos(9x^2).  Functions don't work like that because the cos comes before the multiplying.

Now consider adding another function, 'square' to the sequence of functions.

You could start with x, square it, then times by 3, then find the cosine.  .................................A

Or you could start with x, then times by 3, then find the cosine, then square the result.  ..................................B

If you try these with different values of x, you will find they give different results.  So it is important to show people which you mean when you write the algebra.

A is written like this:

You could write B like this:

but mathematicians have agreed to this shorthand for it:

Putting the squared immediately after the cos should be taken to mean work out the cos first and then square the result.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Trigonometry

If you try these with different values of x, you will find they give different results.  So it is important to show people which you mean when you write the algebra.   
Plese show me and put I don't understand

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Trigonometry

And make graph easier....

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

Here are some values:

I don't know what you mean by an graph in my explanation.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Trigonometry

Graph is function box

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

I have changed the diagram.

Now it shows that x = pi/6 at the start.

The function multiply by 3 is applied, so pi/2 goes into the second function.

The cosine of pi/2 is zero and this is the final output.

You can try this yourself with different inputs

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Trigonometry

Ok I try thaaaank!!!!!

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Malik