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What type of curves does the equation y = a + b cos(x) represent?
What type of curves does the equation y = a + b cos(x) represent?
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Practice Questions
1 question
Q1
What type of curves does the equation y = a + b cos(x) represent?
Linear functions
Cosine waves with varying amplitudes
Parabolas
Exponential functions
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The equation y = a + b cos(x) represents cosine waves with varying amplitudes 'b' and vertical shifts 'a'.
Questions & Step-by-step Solutions
1 item
Q
Q: What type of curves does the equation y = a + b cos(x) represent?
Solution:
The equation y = a + b cos(x) represents cosine waves with varying amplitudes 'b' and vertical shifts 'a'.
Steps: 5
Show Steps
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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