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

What is the period of the function? Give an exact value.
$\square$ units

Question

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

What is the period of the function? Give an exact value.
$\square$ units

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the two points where the function intersects its midline. ‖ ‖ step 2 ⋮ The points given are $\left(\frac{1}{2} \pi, -1 ight)$ and $\left(\frac{5}{4} \pi, -1 ight)$. ‖ ‖ step 3 ⋮ Calculate the distance along the x-axis between these two points to find the period. ‖ ‖ step 4 ⋮ The distance is $\frac{5}{4} \pi - \frac{1}{2} \pi = \frac{5}{4} \pi - \frac{2}{4} \pi = \frac{3}{4} \pi$. ‖ ‖ step 5 ⋮ Since the function intersects its midline twice within one period, the total period is twice the distance calculated. ‖ ‖ step 6 ⋮ The period of the function is $2 imes \frac{3}{4} \pi = \frac{3}{2} \pi$. ‖ ∻[1] Answer∻ ⚹ $\frac{3}{2} \pi$ units ⚹ ∻Key Concept∻ ⚹Period of a Trigonometric Function⚹ ∻Explanation∻ ⚹The period of a trigonometric function is the horizontal length of one complete cycle of the wave. It can be determined by finding the distance between two consecutive points where the function intersects its midline and then multiplying by the number of times the function intersects the midline in one period.◊What is the formula to calculate the period of a trigonometric function given its graph⍭ Generate me a similar question◊⚹

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