arctangent

Examples of arctangent in the following topics:

• Inverse Trigonometric Functions

  • The inverse of sine is arcsine (denoted $\arcsin$), the inverse of cosine is arccosine (denoted $\arccos$), and the inverse of tangent is arctangent (denoted $\arctan$).
  • The arctangent function is a reflection of the tangent function about the line $y = x$.

• Complex numbers and constant coefficient differential equations

  • From Pythagoras' theorem we can see r2 = x2 + y2 and the angle ✓ is just the arctangent of y/x.1.1.4 Forced motion

• Forced motion with damping

  • Figure 1.7: The arctangent function asymptotes at $\pm \pi/2$ , so we should expect to see a phase shift of $\pi$ when going through a resonance.