Amplitude, period, maximum and minimum questions with answers

Questions

1. Question 1Amplitude

   State the amplitude of $y = -4\sin 3x + 3$.

   Show the worked solution

   1. Step 1: Amplitude = |a|: the size of the number in front (always positive)$\text{Amplitude} = 4$
2. Question 2Amplitude

   State the amplitude of $y = 2\sin x$.

   Show the worked solution

   1. Step 1: Amplitude = |a|: the size of the number in front (always positive)$\text{Amplitude} = 2$
3. Question 3Period

   State the period, in degrees, of $y = -4\cos 3x - 2$.

   Show the worked solution

   1. Step 1: Period = (period of the basic graph) ÷ b$\text{Period} = \dfrac{360^\circ}{3}$$\text{Period} = 120^\circ$
4. Question 4Period

   State the period, in degrees, of $y = 3\cos 3x$.

   Show the worked solution

   1. Step 1: Period = (period of the basic graph) ÷ b$\text{Period} = \dfrac{360^\circ}{3}$$\text{Period} = 120^\circ$
5. Question 5Maximum and minimum values

   State the minimum value of $y = 3\cos 2x + 1$.

   Show the worked solution

   1. Step 1: cos goes between −1 and 1$\text{Amplitude} = 3$
   2. Step 2: Minimum = c − amplitude (when the ratio is at its bottom)$\text{Minimum} = 1 - 3$$= -2$
6. Question 6Maximum and minimum values

   State the maximum value of $y = -2\cos 2x + 4$.

   Show the worked solution

   1. Step 1: cos goes between −1 and 1$\text{Amplitude} = 2$
   2. Step 2: Maximum = c + amplitude (when the ratio is at its top)$\text{Maximum} = 4 + 2$$= 6$