Graph sin(2x)

Problem

sin(2*x)

Solution

1. Identify the parent function as y=sin(x) which has an amplitude of 1 and a period of 2*π

2. Determine the amplitude of the given function y=sin(2*x) which is the absolute value of the coefficient of the sine term, |1|=1

3. Calculate the period using the formula P=(2*π)/|b| where b=2

P=(2*π)/2=π

4. Find the key points by dividing the period into four equal intervals of length π/4

5. Evaluate the function at these intervals: (0,0) (π/4,1) (π/2,0) ((3*π)/4,−1) and (π,0)

6. Plot these points on a coordinate plane and connect them with a smooth wave to complete one full cycle.

Final Answer

y=sin(2*x)

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