Writing an Equation In Exercises 83-86, write an equation for the function that is described by the given characteristics. 83. A sine curve with a period of $$ \pi $$, an amplitude of 2 , a right phase shift of $$ \pi / 2 $$, and a vertical translation up 1 unit 84. A sine curve with a period of $$ 4 \pi $$, an amplitude of 3 , a left phase shift of $$ \pi / 4 $$, and a vertical translation down 1 unit 85. A cosine curve with a period of $$ \pi $$, an amplitude of 1 , a left phase shift of $$ \pi $$, and a vertical translation down $$ \frac{3}{2} $$ units 86. A cosine curve with a period of $$ 4 \pi $$, an amplitude of 3 , a right phase shift of $$ \pi / 2 $$, and a vertical translation up 2 units

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Chang Delgado · Accepted Answer

1. $$ f(x) = 2 \sin(2(x + \frac{\pi}{2})) + 1 $$ 2. $$ f(x) = 3 \sin\left(\frac{1}{2}\left(x - \frac{\pi}{4}\right)\right) - 1 $$ 3. $$ f(x) = \cos(2(x - \pi)) - \frac{3}{2} $$ 4. $$ f(x) = 3 \cos\left(\frac{1}{2}(x + \frac{\pi}{2})\right) + 2 $$

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