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Question
Math
Posted 6 months ago

Below is the graph of a trigonometric function. It intersects its midline at (12π,1)\left(\frac{1}{2} \pi,-1\right) and again at (54π,1)\left(\frac{5}{4} \pi,-1\right).

What is the period of the function? Give an exact value.
+x\overline{+\underline{x}} units
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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
Identify the points where the function intersects its midline
step 2
The given points are (12π,1)\left(\frac{1}{2} \pi, -1\right) and (54π,1)\left(\frac{5}{4} \pi, -1\right)
step 3
Calculate the distance in the x-axis between these points to find the period
step 4
The period TT is the difference in the x-coordinates of the points: T=54π12πT = \frac{5}{4} \pi - \frac{1}{2} \pi
step 5
Simplify the expression to find the period: T=54π24π=34πT = \frac{5}{4} \pi - \frac{2}{4} \pi = \frac{3}{4} \pi
[1] Answer
34π\frac{3}{4} \pi units
Key Concept
Period of a Trigonometric Function
Explanation
The period of a trigonometric function is the horizontal length between two consecutive points where the function intersects its midline. It can be found by calculating the difference between the x-coordinates of these points.

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