Sine and cosine graphs
Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Sine and cosine graphs
Sine and cosine graphs are waves that repeat. Every one of them can be written as y = A sin(B(x − C)) + D or y = A cos(B(x − C)) + D, and each letter changes the wave in one way: A stretches it up and down, B squeezes it sideways, C slides it left or right, and D moves the whole wave up or down.
Most questions in this unit go one of two ways. Either you get the equation and find the features (amplitude, period, midline, phase shift), or you get the graph and work back to an equation. The plotting questions ask you to place the five key points of one full wave.
Keep in mind
- Amplitude = |A|, half the distance from the lowest point to the highest point.
- Period = 2π/B, the length of one full wave.
- Midline: y = D, halfway between the top and the bottom.
- Phase shift = C: x − C slides the wave right by C, x + C slides it left.
- Sine starts on the midline going up. Cosine starts at the top.
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