below is the graph of a trigonometric function. it has a maximum point at $\left(\frac{1}{4}\pi, -2.2\
ight)$ and a minimum point at $\left(\frac{3}{4}\pi, -8.5\
ight)$.

what is the amplitude of the function?

Question

below is the graph of a trigonometric function. it has a maximum point at $\left(\frac{1}{4}\pi, -2.2\
ight)$ and a minimum point at $\left(\frac{3}{4}\pi, -8.5\
ight)$.

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": [ "Amplitude and Minimum" ], "new_concepts": [ "Trigonometric Amplitude" ], "current_concepts": [ "Amplitude and Minimum", "Trigonometric Amplitude" ] } ## Identify the maximum and minimum values Using the *Amplitude and Minimum* knowledge point $$ \begin{aligned} &y_{\text{max}} = -2.2\ &y_{\text{min}} = -8.5 \end{aligned} $$ ## Calculate the amplitude Using the *Amplitude and Minimum* knowledge point $$ \begin{aligned} A &= \frac{y_{\text{max}} - y_{\text{min}}}{2}\ A &= \frac{-2.2 - (-8.5)}{2}\ A &= \frac{6.3}{2}\ A &= 3.15 \end{aligned} $$ 3.15 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Amplitude" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the maximum and minimum values

Calculate the amplitude

Answer: