Question

Construct the equations of the following trigonometric functions:
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A sine function with amplitude 2, period pi, phase shift pi/3 right
A tangent function with a reflection in the y-axis, period ¾, translation up 5 units
A cosine function with period 270°, translation down 50 units, reflection in the x-axis.

Answer 1

Do you understand what each of A, B, C and D do in the general form
\(\Large y=A\sin[B(x-C)]+D\) ?

Your text might use different letters, but you should understand how A, B, C and D affect the sine function (and similarly for tangent and cosine - just replace the function name).

Answer 2

|A| gives you stretches/shrinks, and if A<0 you get a reflection over the x-axis

B gives you a period change, where the period for sine and cosine = \(2\pi/B\) and for tangent period =\(\pi/B\)

Also if B<0, then you get a reflection over the y-axis.

C gives you a horizontal shift, to the right if C>0 and to the left if C<0.

D gives you a vertical shift, up if D>0 and down if D<0.