For piston B find the time (t) when Piston B first reaches a minimum distance from the origin (O). Express as an exact value and show all algebraic working.
I am sorry could not attach the graph but this is the equation:y_2=2 sin 3(t-π/12)+8
I am sorry could not attach the graph but this is the equation:y_2=2 sin 3(t-π/12)+8
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So that's the sine of 3(t - pi/12)?
That means it's the graph of sin(3t), shifted to the right by pi/12 seconds. The +8 means that it's also shifted upward by 8 units. Since the amplitude is 2, then it varies from 8-2 to 8+2, that is from 6 to 10.
So the minimum distance is when it equals 6, which is at the minimum of the sine wave. The first minimum of sin(x), the value sin(x) = -1, is when x = pi, so this will happen when 3(t - pi/12) = pi. Solve for t.
That means it's the graph of sin(3t), shifted to the right by pi/12 seconds. The +8 means that it's also shifted upward by 8 units. Since the amplitude is 2, then it varies from 8-2 to 8+2, that is from 6 to 10.
So the minimum distance is when it equals 6, which is at the minimum of the sine wave. The first minimum of sin(x), the value sin(x) = -1, is when x = pi, so this will happen when 3(t - pi/12) = pi. Solve for t.