below is the graph of a trigonometric function. it intersects its midline at $-\frac{7}{8}\pi, -10.1$, and it has a maximum point at $-\frac{1}{2}\pi, -2.7$.

what is the amplitude of the function?

Question

below is the graph of a trigonometric function. it intersects its midline at $-\frac{7}{8}\pi, -10.1$, and it has a maximum point at $-\frac{1}{2}\pi, -2.7$.

what is the amplitude of the function?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Midline", "Trigonometric Amplitude" ], "new_concepts": [], "current_concepts": [ "Trigonometric Midline", "Trigonometric Amplitude" ] } ## Identify the midline and maximum value Using the *Trigonometric Midline* knowledge point $$ \begin{aligned} &y_{\text{midline}} = -10.1\ &y_{\text{max}} = -2.7 \end{aligned} $$ ## Calculate the amplitude Using the *Trigonometric Amplitude* knowledge point $$ \begin{aligned} A &= y_{\text{max}} - y_{\text{midline}}\ A &= -2.7 - (-10.1)\ A &= 7.4 \end{aligned} $$ 7.4 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Amplitude" ] }

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Question

Explanation:

Identify the midline and maximum value

Calculate the amplitude

Answer: