Question

2/5=4/5sec(x) which is equivalent to pi/3 but how

Answer 1

I am viewing my own problem now

Answer 2

So first off you can move the 4/5 to the other side of the equals sign and get:

\[\sec x = \frac{\frac{2}{5}}{\frac{4}{5}} = \frac{1}{2}\]

We know that \(\sec x\) is the same as \(\frac{1}{\cos x}\), which means that:

\[ \frac{1}{\cos x} = \frac{1}{2} \]

We can invert both sides and get:

\[ \cos x = 2 \]

However, this does not make \(x\) be \(\frac{\pi}{3}\), so I don't know why you were told it was. Or did I misunderstand what you said about \(\frac{\pi}{3}\)?

Answer 3

Is it possible that the OP wrote the problem wrong? If s/he had 4/5 = 2/5 sec x, then we have sec x = 2, which is equivalent to cos x = 1/2, and those DO give us x = π/3.

Answer 4

I hope so :) That's roughly what I was noticing.