How’d the test go?!?

• Pg. 385 #43,44, 46, 51 (use calculator to rewrite as a sinusoid)

#9, 10, 35-38 allMemorization quiz through inverse trig functions on Friday!!

7.1 Transformations and Trigonometric Graphs

Review of Transformations• If y = f(x) is the original

graph, what do the following do?

• y = af(x)• y = -f(x)• y = f(x + c)• y = f(x – c)• y = f(x) + d • y = f(x) – d • y = f(-x)

Sinusoids• A sinusoid is a function that can

be written in the formf(x) = asin(bx + c) + dwhere a, b, c, and d are real numbers.

• The graph of a sinusoid can be obtained from the graph of y = sin x by a combination of horizontal stretching or shrinking, horizontal shifting, vertical stretching or shrinking and vertical shifting.

7.1 Transformations and Trigonometric Graphs

Sums that are Sinusoidal• For all real numbers a and

b, the functionf(x) = asin x + bcos x is a sinusoid. In particular, there exist real numbers A and α such thatasin x + bcos x = Asin (x + α),where |A| is the amplitude and α is the phase shift.

Practicing Sinusoids• Show that

f(x) = 2sin x + 5cos x is a sinusoid. Also, approximate A and α so that Asin (x + α) = 2sin x + 5cos x

7.1 Transformations and Trigonometric Graphs

Sums that are Sinusoidal• For all real numbers a, b, d,

h, k the functionf(x) = asin (bx + h) + dcos (bx + k) is a sinusoid. In particular, there exist real numbers A and α such that asin (bx + h) + dcos (bx + k) = Asin (bx + α)

Practicing Sinusoids• Show that

f(x) = 3sin (2x – 1) + 4cos (2x + 3) is a sinusoid. Also, approximate A and α so that Asin (2x + α) = 3sin (2x – 1) + 4cos (2x + 3)

7.1 Transformations and Trigonometric Graphs

Practicing Sinusoids• Show that

f(x) = sin (2x) + cos (3x) is not sinusoidal. Also, find the domain, range, and period of f.

• Decide which of the following are sinusoids. If f(x) is a sinusoid, determine A and α.

2sin 3 1 5cos 3 2y x x sin 3 1 3cos 3 2y x x

3sin 4 1 2cos 2 3y x x

3sin 2 0.5 cos 2 1y x x

2sin 3 2 3cos 3 4y x x

2sin 2 3cos 4 1y x x