For y=asin(bx)+c or y=acos(bx)+c, a,b 0: Midline: y=c =|a| T= 2pi|b| or 360 |b| y_max=c+|a| y_min=c-|a| The sketches below use a,b>0. **Equation** | **Midline** | **Amplitude** | **Maximum and minimum** | **Period** y=3sin 2x+1 | y=1 | 3 | 1+3=4 1-3=-2 | 180 or pi y=5-2cos(x)/(2) | y=5 | 2 | 5+2=7 5-2=3 | 720 or 4pi Example: y=2cos3x-1, 0 <= x <= pi **Feature** | **Working** Midline | y=-1 Amplitude | 2 Maximum and minimum | -1+2=1 -1-2=-3 Period | 2pi3 Start point | x=0: y=2cos 0-1=1 Mark the midline and extremes, plot at quarter-period intervals, then stop at both endpoints.

For \(y=a\sin(bx)+c\) or \(y=a\cos(bx)+c\), \(a,b\ne0\):

\(\text{Midline: }y=c\qquad\text{Amplitude}=|a|\qquad T=\dfrac{2\pi}{|b|}\text{ or }\dfrac{360^\circ}{|b|}\)

Example: \(y=2\cos3x-1\), \(0\le x\le\pi\)

Mark the midline and extremes, plot at quarter-period intervals, then stop at both endpoints.

Trigonometry

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Sketching of \(y=a\sin \left( bx \right)+c\) and \(y=a\cos \left( bx \right)+c\)

Sketching of \(y=a\sin \left( bx \right)+c\) and \(y=a\cos \left( bx \right)+c\)

Video Solution:

Solution:

Solution locked