Sunday

April 20, 2014

April 20, 2014

Posted by **Sam** on Thursday, October 31, 2013 at 8:11am.

(a) Find a sequence of buttons that will transform x into 1/x.

(b) Find a sequence of buttons that will transform sqrt(x) into sqrt(x+1).

A calculator is broken so that the only keys that still work are the \sin, \cos, \tan, \cot, \sin^{-1}, \cos^{-1}, and \tan^{-1} buttons. The display initially shows 0. In this problem, we will prove that given any positive rational number q, show that pressing some finite sequence of buttons will yield q. (Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.)

(a) Find a sequence of buttons that will transform x into \frac{1}{x}.

(b) Find a sequence of buttons that will transform \sqrt x into \sqrt{x+1}.

(c) Now show that you can get any positive rational number.

Thanks for all the help before it was really appreciated :) But I have trouble trying to do these questions: if you can only answer one that's fine but I kinda need help. Thanks.

- Trigonometry -
**Steve**, Thursday, October 31, 2013 at 10:47amI assume that the calculator initially displays q.

What's wrong with tan(arctan(q)) ?

cot(arctan(q)) = 1/q

A triangle with legs 1 and √x has hypotenuse √(x+1) so,

cos(arctan(√x)) = 1/√(x+1)

Now just convert that into its reciprocal, as above.

- Trigonometry -
**Sam**, Thursday, October 31, 2013 at 10:54amThanks a lot man ^_^ Much appreciated :)

**Related Questions**

math - Suppose that the multiplication and division keys on your calculator were...

Math - Roger knows how many keys a piano has. He knows that some of the keys are...

Math - Roger knows how many keys a piano has. He knows that some of the keys are...

Math - Only the 1, +, -, X, / , (, ), and = keys on a scientific calculator are ...

math - the inverse cosine of negative 0.947 Put it in your calculator... The ...

Trigonometry college - Use a calculator to solve csc (theta) = -3. I know the ...

trigonometry - How do you draw only the top half of a circle in parametric mode ...

Physics - A building superintendent twirls a set of keys in a circle at the end ...

physics - A student throws a set of keys vertically upward to his fraternity ...

physics - A student throws a set of keys vertically upward to her sorority ...