Graphs Of Trigonometric Functions
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Graphs of trigonometric functions – Transformations Consider the sine function y = a sin(bx ± c ) ± d , where a, b > 0 and c, d ≥ 0 :
The parameter a affects the amplitude of the sine curve which now becomes equal to a. - The curve stretches (a>1)/compresses (0
(
)
(90 , a )
and its minimum point is at
-a causes the curve to reflect with respect to the x-axis.
The parameter b affects the period T of the sine curve. Now, T =
360 . b
The curve contracts (b rel="nofollow">1)/expands (0
,1 and its minimum
-b causes the curve to reflect with respect to the y-axis.
The parameter c° causes the curve to slide along the x-axis. +c° causes a horizontal shift (translation) of the curve to the left. -c° causes a horizontal shift (translation) of the curve to the right. The curve’s maximum point is now located at point at 270 ± c ,−1 .
(
)
(90
)
± c ,1
and its minimum
Finally, the parameter d causes the curve to slide upwards (+d)/downwards (-d) along the y-axis, i.e. it causes a vertical translation of the curve. The curve’s maximum point is now located at point at 270 ,−1 ± d .
(
)
(90 ,1 ± d )
and its minimum
The curve’s central line is now y = ± d . COMBINE THE ABOVE INFORMATION TO SKETCH THE GRAPHS OF COMPLEX TRIGONOMETRIC EQUATIONS!
The parameter a affects the amplitude of the sine curve which now becomes equal to a. - The curve stretches (a>1)/compresses (0
(
)
(90 , a )
and its minimum point is at
-a causes the curve to reflect with respect to the x-axis.
The parameter b affects the period T of the sine curve. Now, T =
360 . b
The curve contracts (b rel="nofollow">1)/expands (0
,1 and its minimum
-b causes the curve to reflect with respect to the y-axis.
The parameter c° causes the curve to slide along the x-axis. +c° causes a horizontal shift (translation) of the curve to the left. -c° causes a horizontal shift (translation) of the curve to the right. The curve’s maximum point is now located at point at 270 ± c ,−1 .
(
)
(90
)
± c ,1
and its minimum
Finally, the parameter d causes the curve to slide upwards (+d)/downwards (-d) along the y-axis, i.e. it causes a vertical translation of the curve. The curve’s maximum point is now located at point at 270 ,−1 ± d .
(
)
(90 ,1 ± d )
and its minimum
The curve’s central line is now y = ± d . COMBINE THE ABOVE INFORMATION TO SKETCH THE GRAPHS OF COMPLEX TRIGONOMETRIC EQUATIONS!
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