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April 19, 2014

April 19, 2014

Posted by **edwin** on Saturday, February 6, 2010 at 8:01pm.

I know the answer is .322

but I don't know how to arrive at the answer.

- calculus -
**Damon**, Saturday, February 6, 2010 at 8:14pmI do not think so in either degrees or radians.

- calculus -
**MathMate**, Saturday, February 6, 2010 at 8:21pmMost of us take the calculator and get the answer 0.322398.

The fact that you asked how to get the answer suggests to me that you'd like to do the calculations yourself.

You can do this by expansion of the tan(x) function which involves the evaluation of Bernoulli numbers. If we take advantage of the fact that 1+tan²(x)=sec(x)², or

tan²(x)=sec(x)²-1

we only need to evaluate cos(x), which is given algebraically as:

cos(x)=1-x²/2!+x^{4}/4!-....

- calculus -
**MathMate**, Saturday, February 6, 2010 at 8:23pmadditional note:

Since tan(x)=tan(x±π), you can calculate tan(x-π) instead of tan(x).

This way, the cosine series converges more rapidly.

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