Curve or Straight?

Calculus Level 3

Given that,

$\sin (x-y) = \cos (y-x)$

Does the graph have curve(s)?

No, it has infinitely many lines with gradient -1 each. No, it is a straight line with gradient 1. Yes, it has infinitely many curves. Yes, it has a curve. No, it is a straight line with gradient -1. No, it has infinitely many lines with gradient 1 each. No, it is a straight line parallel to the x-axis. No, it is a straight line parallel to the y-axis.

1 solution

Haziman Sairin
Feb 25, 2018

$\sin (x-y) = \cos (y-x)$

$\sin (x-y) = \cos (x-y)$

$\dfrac{\sin (x-y)}{\cos (x - y)} = 1$

$\tan (x-y) = 1$

$x - y = \tan^{-1} 1$

$x - y = \pi/4$

$y = x - \pi/4$

$\dfrac{dy}{dx} = 1$

Since $\boxed{\tan^{-1} 1}$ maps to infinitely many periodic angles (the angle above is one of them), the graph has infinitely many lines with gradient 1 each .

Curve or Straight?

1 solution

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