Question

Math

Posted 6 months ago

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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.
$\overline{+\underline{x}}$ 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 $\left(\frac{1}{2} \pi, -1\right)$ and $\left(\frac{5}{4} \pi, -1\right)$

step 3

Calculate the distance in the x-axis between these points to find the period

step 4

The period $T$ is the difference in the x-coordinates of the points: $T = \frac{5}{4} \pi - \frac{1}{2} \pi$

step 5

Simplify the expression to find the period: $T = \frac{5}{4} \pi - \frac{2}{4} \pi = \frac{3}{4} \pi$

[1] Answer

$\frac{3}{4} \pi$ 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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