The next turning points are π∕2 + π next is π∕2 + 2π the next is π∕2 + 3π
The generalized math statement is that the turning points of a sine function are π∕2 + kπ where k is any integer.
What are the turning points y = sin 3x? in the interval -π < x < π (The period of this function is 2π∕3)
To find the turning points 3x must equal π∕2 + kπ Let k = 0 and therefore 3x = π∕2 So x = π∕2 ÷ 3 = π∕6
So y = sin 3x has a turning point at (π∕6, 1) The amplitude determines the second coordinate of the ordered pair.
The next turning point is when k = 1. So 3x = π∕2 + 1π x = π∕6 + π/3 x = 3 π∕6 = π∕2
So y = sin 3x has a turning point at (π∕2, -1)
The next turning point is when k = 2. So 3x = π∕2 + 2π x = π∕6 + 2π/3 x = 5 π∕6
So y = sin 3x has a turning point at (5π∕6, 1)
The next turning point is when k = 3. So 3x = π∕2 + 3π x = π∕6 + π which is outside the interval -π < x < π
The next turning point is when k = -1. So 3x = π∕2 - 1π x = π∕6 - π/3 x = - π∕6
So y = sin 3x has a turning point at (-π∕6, -1)
The next turning point is when k = -2. So 3x = π∕2 - 2π x = π∕6 - 2π/3 x = -π∕2
So y = sin 3x has a turning point at (-π∕2, 1)
The next turning point is when k = -3. So 3x = π∕2 - 3π x = π∕6 - π x = -5π∕6
So y = sin 3x has a turning point at (-5π∕6, -1)
The next turning point is when k = -4. So 3x = π∕2 - 4π x = π∕6 - 4π∕3 = -7π∕6 which is outside the interval -π < x < π
The below graph is of y = sin 3x Use the graph to check the results.
return PCTC