question 27 of 40

in $\delta def$, $\sin d = \frac{36}{39}$. what is $\cos e$?

a. $\frac{36}{39}$
b. $\frac{39}{15}$
c. $\frac{15}{36}$
d. $\frac{15}{39}$

Question

question 27 of 40

in $\delta def$, $\sin d = \frac{36}{39}$. what is $\cos e$?

a. $\frac{36}{39}$
b. $\frac{39}{15}$
c. $\frac{15}{36}$
d. $\frac{15}{39}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios", "Sine Ratio" ], "new_concepts": [ "Cosine Ratio", "Cofunction Identities" ], "current_concepts": [ "Trigonometric Ratios", "Sine Ratio", "Cosine Ratio", "Cofunction Identities" ] } ## Identify the given values and target ratio $$ \begin{aligned} &\triangle DEF \text{ is a right triangle with } \angle F = 90^\circ\ &DE = 39 \quad (\text{hypotenuse})\ &DF = 15 \quad (\text{adjacent to } \angle D, \text{ opposite to } \angle E)\ &\sin D = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{EF}{DE} = \frac{36}{39} \implies EF = 36 \end{aligned} $$ ## Apply the definition of cosine for angle E $$ \begin{aligned} &\cos E = \frac{\text{Adjacent to } \angle E}{\text{Hypotenuse}} = \frac{EF}{DE}\ &\cos E = \frac{36}{39} \end{aligned} $$ ## Verify using cofunction identity $$ \begin{aligned} &D + E = 90^\circ\ &\cos E = \sin(90^\circ - E) = \sin D = \frac{36}{39} \end{aligned} $$

A. $\frac{36}{39}$

B. $\frac{39}{15}$

C. $\frac{15}{36}$

D. $\frac{15}{39}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and target ratio

Apply the definition of cosine for angle E

Verify using cofunction identity

Answer: