How do you calculate $cos(tan^-1 (-12 / 5))$ ?

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Answer 1 · 2015-05-15T19:04:38

If you have a graphing calculator, you can simply punch in the equation.
I am using the TI-84 Plus with it in 'degree mode'

When I put in
The equation listed above I got the answer of .3846153846
Which would be rounded to .385 or .38 degrees.

Answer 2 · 2015-05-15T23:42:00

A triangle with sides $5$ , $12$ and $13$ is a right angled triangle, since $5^2 + 12^2 = 25 + 144 = 169 = 13^2$ .

Let us use $theta$ to denote the (second largest) angle between the side of length $5$ and the hypotenuse - which has length $13$ .

Then $tan theta = 12/5$ and $cos theta = 12/13$

$tan (-theta) = -tan theta = -12/5$

So $tan^(-1)(-12/5) = -theta$

and $cos(tan^(-1)(-12/5)) = cos(-theta) = cos(theta) = 12/13$

How do you calculate cos(tan^-1 (-12 / 5))cos(tan^-1 (-12 / 5))?