Question

write tan (arc cos x/3) in algebraic form. i have no idea what arc is so i definetely need help on the explanation

Answer 1

arc cos is the same as:
\[\cos^{-1}\]
or inverse cos.

Answer 2

oh ok thanks

Answer 3

so then i get tan (cos^-1 x/3). then what?

Answer 4

normally i would draw you a picture, but im at a school computer atm >.<
first you need to note that inverse trig functions return angles, so we should have:
\[\cos^{-1}(\frac{x}{3}) = \theta \Rightarrow \cos(\theta) = \frac{x}{3}\]
Then what you want to do is draw a right triangle, with the angle theta somewhere in it. Since the cos of the angle is x/3, the hypotenuse of the right triangle will be 3, and the side adjacent of the angle will be x. Then you use pythagorean theorem to see what the remaining side is. and then finally you can solve for tan of the angle, it would be opposite/adjacent.

Answer 5

how do you use pythagorean theorem with 2 variables?