How do you find the exact value of cos[arc tan(-2/3)]?

2 Answers
Jun 12, 2015

The exact value is apparently 3/sqrt(13).

However, you'll have to use a calculator to find arctan(-2/3). It's an irrational radian value that you'll get to be -33.69006752598...etc^o. Wolfram Alpha simply gives it as:

-180/pi * arctan(-2/3)
which doesn't really give a satisfactory exact answer (such as 2/sqrt2). It's just the conversion of arctan(-2/3) to degrees...

If you just take this exact result and take the cos of it, you'll get 3/sqrt(13), but it probably won't be obvious at all that it's equal to that from just looking at it.

sqrt13 = 3.605551275...etc.

3/sqrt13 ~~ 0.83205...etc

Jun 14, 2015

Find cos (arctan (-2/3))

Explanation:

tan x = -2/3

Calculator gives; x = -33.69 and x = -33.69 + 180 = 146.31

Therefor, cos x = +- 0.83