4.1.3 quiz: trigonometric ratios

a. $\frac{24}{7}$
b. $\frac{7}{24}$
c. $\frac{25}{7}$
d. $\frac{24}{25}$
e. $\frac{25}{24}$
f. $\frac{7}{25}$

Question

4.1.3 quiz: trigonometric ratios

a. $\frac{24}{7}$
b. $\frac{7}{24}$
c. $\frac{25}{7}$
d. $\frac{24}{25}$
e. $\frac{25}{24}$
f. $\frac{7}{25}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios", "Sine Ratio", "Tangent Ratio" ], "new_concepts": [ "Cosine Ratio" ], "current_concepts": [ "Trigonometric Ratios", "Sine Ratio", "Tangent Ratio", "Cosine Ratio" ] } ## Identify the given side lengths and angles Using the *Trigonometric Ratios* knowledge point $$ \begin{aligned} &\text{Hypotenuse} = 25\ &\text{Side opposite to } 16^\circ = 7\ &\text{Side adjacent to } 16^\circ = 24 \end{aligned} $$ ## Determine the target trigonometric ratio Using the *Sine Ratio* and *Tangent Ratio* knowledge points $$ \begin{aligned} &\sin(16^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{7}{25}\ &\cos(16^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{24}{25}\ &\tan(16^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{7}{24} \end{aligned} $$ ## Match with the given options Using the *Trigonometric Ratios* knowledge point $$ \begin{aligned} &\text{Option F represents } \frac{7}{25} = \sin(16^\circ) \end{aligned} $$

A. $\frac{24}{7}$

B. $\frac{7}{24}$

C. $\frac{25}{7}$

D. $\frac{24}{25}$

E. $\frac{25}{24}$

F. $\frac{7}{25}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Ratios" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given side lengths and angles

Determine the target trigonometric ratio

Match with the given options

Answer: