Pre-Calculus

Cards (10)

• 1
  Front

  What is the effect of the transformation y = f(x - h) + k on the graph of y = f(x)?

  Back

  The graph shifts h units horizontally (right if h > 0, left if h < 0) and k units vertically (up if k > 0, down if k < 0).

• 2
  Front

  State the Pythagorean trigonometric identity.

  Back

  sin²(θ) + cos²(θ) = 1

• 3
  Front

  What are the coordinates of the point on the unit circle corresponding to the angle θ?

  Back

  (cos θ, sin θ)

• 4
  Front

  How is the magnitude (length) of a vector v = ⟨a, b⟩ calculated?

  Back

  |v| = √(a² + b²)

• 5
  Front

  How do you convert polar coordinates (r, θ) to rectangular (Cartesian) coordinates?

  Back

  x = r cos θ and y = r sin θ

• 6
  Front

  In parametric equations, what does the parameter t typically represent?

  Back

  An independent variable (often time) that determines both x and y coordinates simultaneously as t varies.

• 7
  Front

  What does it mean for a limit lim(x→c) f(x) = L?

  Back

  As x approaches c (but does not equal c), the values of f(x) get arbitrarily close to L.

• 8
  Front

  What is the double-angle identity for sin(2θ)?

  Back

  sin(2θ) = 2 sin(θ) cos(θ)

• 9
  Front

  What is the dot product of vectors u = ⟨a, b⟩ and v = ⟨c, d⟩, and what does a result of 0 indicate?

  Back

  u · v = ac + bd; a result of 0 means the vectors are perpendicular (orthogonal).

• 10
  Front

  How do you convert rectangular coordinates (x, y) to polar coordinates (r, θ)?

  Back

  r = √(x² + y²) and θ = arctan(y/x), adjusting the quadrant of θ as needed.