Math Is Fun Forum

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: (Less than) 21 Trig Questions from Amrita

I thought I'd shown how to do this.

Any equation of the form

can be re-written as a sine or cosine function.  First find R like this

In your example R = 10

Then proceed like this:

Now, if you want a sine function put alpha = arctan (b/a) so that

So

In your example c/R = 0.9  so you can arcsin this and subtract alpha to get x.

From the known shape of the sine curve (you don't need to plot it) you'll find two values of x in the specified domain.

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: (Less than) 21 Trig Questions from Amrita

Didn't we already solve that one without plotting?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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Re: (Less than) 21 Trig Questions from Amrita

I am getting

0.6 cos(x) + 0.8 sin(x) = 0.9

But, I do not know the arcsines of 0.6 or the arccos of 0.8

By the way, I am not particularly interested in x. We want the sine of the sum of the two values of x

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: (Less than) 21 Trig Questions from Amrita

I thought I'd done this already.  See posts 75 and 76.

You don't need an accurate graph for this; a sketch will do; and you can fully answer the question without a calculator.

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: (Less than) 21 Trig Questions from Amrita

But we want sine((a+b)/2).  You can use the function grapher like I did to find this x value and hence its sine, or (challenge) do it by considering the displacement of this graph from the standard sine curve.  Once you have that you can get cosine((a+b)/2) and hence sine(a+b)

Bob

graph below.

http://i.imgur.com/1kQt0HA.gif

I am sorry, I am very confused. How do I find (a+b)/2 analytically? Is there any explanation where I won't need graph? (i do not think my teacher will accept this)

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: (Less than) 21 Trig Questions from Amrita

You can sketch the graph of

It will be a standard sine curve, displaced to the left by angle alpha.  Let's call it graph one.  Post 75 shows this.

The line y = 0.9 will cut the curve in two places, a and b.  Because the curve has a line of symmetry at the maximum value, we can locate this value of x as (a+b)/2, ie. half way between a and b.

The next post shows  graph two:

together with graph one.  Remember that graph one is just graph two, shifted left by angle alpha.

The maximum for graph two is at x = pi/2  so the maximum for graph one is at pi/2 - alpha.

So (a+b)/2 = pi/2 - alpha.

and

Using the double angle formula

Will your teacher accept that ?  I would

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: (Less than) 21 Trig Questions from Amrita

Thanks for your time. I will go and have my lunch so that I am well nourished enough to attempt comprehension of this.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: (Less than) 21 Trig Questions from Amrita

In the Jeeves books, P G Wodehouse recommends fish for making you brainy.  If you haven't read any, I strongly recommend them for a good laugh.

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