below is the graph of a trigonometric function. it has a minimum point at $(-5.4, 1.25)$ and a maximum point at $(7.4, 6.75)$.

what is the period of the function? give an exact value.

Question

below is the graph of a trigonometric function. it has a minimum point at $(-5.4, 1.25)$ and a maximum point at $(7.4, 6.75)$.

what is the period of the function? give an exact value.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Period" ], "new_concepts": [], "current_concepts": [ "Trigonometric Period", "Amplitude and Minimum", "Trigonometric Midline" ] } ## Identify the given extrema coordinates Using the *Trigonometric Period* knowledge point $$ \begin{aligned} &x_{\text{min}} = -5.4\ &x_{\text{max}} = 7.4 \end{aligned} $$ ## Calculate the horizontal distance between extrema Using the *Trigonometric Period* knowledge point $$ \Delta x = 7.4 - (-5.4) = 12.8 $$ ## Determine the period of the function Using the *Trigonometric Period* knowledge point $$ \begin{aligned} &\frac{T}{2} = \Delta x = 12.8\ &T = 2 \times 12.8 = 25.6 \end{aligned} $$ $25.6$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Period" ] }

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Question

Explanation:

Identify the given extrema coordinates

Calculate the horizontal distance between extrema

Determine the period of the function

Answer: