Categories Exact Values of Trig Functions Trigonometric Functions cos[arctan(5/7)]… Post author By mpershan Post date November 18, 2013 4 Comments on cos[arctan(5/7)]… What’s up with this cool work? via Tina Share this:EmailPrint ← “Perimeter is the space outside of a shape.” → Fractions Mistakes In The Wild 4 replies on “cos[arctan(5/7)]…” So we start with tan (arctan (5/7)), then we’ve got cot(arctan(5/7)) = 7/5 That’s reassuring and logical. Then we have cot(arctan(5/7))*sin(arctan(7/5)) = cos(arctan(5/7)) Since cotx = cosx/sinx the student extended that to any input x – in this case the input is the complicated arctan(5/7) Generally true? Is it even true in this case? I like that the student seems to understand that the input of arctan(5/7) is an angle input. It’s definitely progress. Now square both sides and you’re almost there! I like this approach, one good way to start the problem. I wish that the kid would learn that you should draw a triangle or a unit circle whenever you’re stuck on a trig problem of any sort. Algebraically, though, barryrsmith’s idea of squaring both sides next is a good way to proceed. I expected students to solve this by drawing a triangle, but thought it was interesting what he came up with when he forgot that approach! Comments are closed.