Unit 10: Trigonometric Graphs

Key words

• AmplitudeKey word · Unit 10AmplitudeHalf the distance between a wave’s highest and lowest outputs.Exactly: For $y=A\sin (B(x-C))+D$ or $y=A\cos (B(x-C))+D$, amplitude is $|A|$, with $B\ne 0$.Mix-up alert: Amplitude is always nonnegative and is not the vertical shift.See this in Key wordsClose meaning
• PeriodKey word · Unit 10PeriodThe shortest positive input shift that repeats the whole pattern.Exactly: A fundamental period $P>0$ satisfies $f(x+P)=f(x)$ wherever defined, with no smaller positive period.Mix-up alert: For a nonconstant transformed sine or cosine, the period is $\frac{2\pi }{|B|}$; for tangent it is $\frac{\pi }{|B|}$.See this in Key wordsClose meaning
• Phase shiftKey word · Unit 10Phase shiftA horizontal shift of a repeating graph.Exactly: In A sin(B(x-C))+D or A cos(B(x-C))+D, the phase shift is C, with B nonzero.Mix-up alert: Factor $B$ before reading the shift in $Bx-c=B(x-\frac{c}{B})$. The shift is $\frac{c}{B}$, with $B\ne 0$.See this in Key wordsClose meaning
• MidlineKey word · Unit 10MidlineThe horizontal line halfway between a wave’s high and low values.Exactly: For $y=A\sin (B(x-C))+D$ or $y=A\cos (B(x-C))+D$, the midline is $y=D$.Mix-up alert: The midline is an output value, while amplitude measures distance from it.See this in Key wordsClose meaning
• FrequencyKey word · Unit 10FrequencyThe number of complete cycles per unit of input.Exactly: For a sinusoid with period $T>0$, ordinary frequency is $\frac{1}{T}=\frac{|B|}{2\pi }$ cycles per input unit.Mix-up alert: B is angular frequency in radians per input unit, not usually the number of cycles.See this in Key wordsClose meaning