What is the value of tan (Arc cos 15 seventeenths)?

Question

1. 8/15
2. 8/17
3. 15/8
4. 17/8
Can you guys explain what the Arc means?

Answer 1

suppose you have:
cos 60° = 1/2 , we know that
then arc cos(1/2) = 60°
other notations are: cos^-1 (1/2) = 60°
So, arc cos and cos are inverse operations.
On your calculator you will notice that each trig function
has its inverse after pressing 2ndF
e.g. enter
sin 45° , you will get .707106...
now press 2ndF, sin, and you will get back your 45°

so, to your question,
look at the Arc cos 15 seventeenths or, I assume you meant: arc cos (15/17)
This means you are looking for an angle Ø so that cosØ = 15/17
sketch a right-angled triangle with base angle Ø, hypotenuse of 17, and adjacent side of 15
by Pythagoras: 15^2 + y^2 = 17^2
y^2 = 64
y = √64 = 8

then tan (Arc cos (15/17)) = tanØ = opposite/adjacent = 8/15 or .5333...

Verification on my calculator
15/17
=
2ndF cos
=
tan
=
I got .53333..