How would I find the exact value of this?

Question

cos(tan^-1(-5/12)) I know I would write a triangle but I have no clue where to start. Thank you!

Answer 1

There are 2 answers...

We are asked to find the cosine of the angle whose tangent is -5/12.

The tangent is negative in quadrants 2 and 4...

in quadrant 2, opposite = 5 and adjacent = -12. The hypotenuse is

then 13 by pythagorean.

the cosine is therefore, -12/13 <note that cosine is negative in quadrant 2>

in qaudrant 4, opposite = -5 and adjacent = 12. Again the hypotenuse

is 13. The cosine is 12/13 <note that cosine is positive in quadrant 4>

Answer 2

the angle whose tangent is -5/12 is in either the 2nd or 4th quadrant

tanx = opposite side/adjacent side = o/a where o = -5 and a = 12 or o =5 and a =-12

cosx = adjacent side/hypotenuse = 12/13 or -12/13

hypotenuse = 13

h^2 = a^2 + o^2 = 5^2 + 12^2 = 25 + 144 = 169

h= sqr169 = 13

cosx = 12/13 or -12/13