Trigonometric function transformation Revision

Revision on trigonometric Function Transformation

Lesson objectives
(CCSS.MATH.CONTENT.HSF.IF.C.7.E
CCSS.MATH.CONTENT.HSF.TF.A.3)

1) Students will construct and analyze the graphs of trig functions
2)Graph the sine and cosine functions.
3) Analyze the graph of a sine or cosine function to determine the amplitude, period, and transformations (translation and reflection).
4) Analyze the equation of a sine or cosine function to determine the amplitude, period, and transformations (translation and reflection).

Remember 😃

Reflecting
What transformations affect each of the following characteristics of a sinusoidal function?
i) period
ii) amplitude
iii) equation of the axis

State the period, amplitude, horizontal translation, and equation of the axis for each of the following trigonometric functions.

Fill in the Blanks

As a dolphin swims along by the side of a cruise ship he jumps to a height of four meters above the water surface and dives to a depth of four meters below the surface. He does this in a regular motion (simple harmonic motion). A passenger using a stopwatch and starting it just as the dolphin is at the surface determines that the dolphin completes one cycle every 8 seconds. a. Describe the displacement of the dolphin relative to the water surface using a sinusoid curve and sketch the graph of the dolphin’s displacement relative to the water surface b After three seconds how high above the surface is the dolphin? c Is the dolphin above or below the surface of the water after 37 seconds?