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What type of curves does the equation y = a + b cos(x) represent?

Practice Questions

Q1
What type of curves does the equation y = a + b cos(x) represent?
  1. Linear functions
  2. Cosine waves with varying amplitudes
  3. Parabolas
  4. Exponential functions

Questions & Step-by-Step Solutions

What type of curves does the equation y = a + b cos(x) represent?
  • Step 1: Identify the equation given, which is y = a + b cos(x).
  • Step 2: Recognize that 'cos(x)' is a cosine function, which produces a wave-like pattern.
  • Step 3: Understand that 'b' affects the height of the wave, known as the amplitude. A larger 'b' means a taller wave.
  • Step 4: Note that 'a' shifts the entire wave up or down. If 'a' is positive, the wave moves up; if negative, it moves down.
  • Step 5: Conclude that the equation represents cosine waves that can vary in height and position based on the values of 'a' and 'b'.
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