suppose the vector $\mathbf{s}$ has magnitude 93 and makes an angle of $220^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{s}$ is in standard position.

write $\mathbf{s}$ in the form $\mathbf{s} = a\mathbf{i} + b\mathbf{j}$.

do not round any intermediate computations, and round the values in your answer to the nearest hundredth.

Question

suppose the vector $\mathbf{s}$ has magnitude 93 and makes an angle of $220^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{s}$ is in standard position.

write $\mathbf{s}$ in the form $\mathbf{s} = a\mathbf{i} + b\mathbf{j}$.

do not round any intermediate computations, and round the values in your answer to the nearest hundredth.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vector Components", "Trigonometric Resolution" ], "new_concepts": [], "current_concepts": [ "Vector Components", "Trigonometric Resolution", "Vector Representation" ] } ## Identify vector parameters Using the *Vector Components* knowledge point $$ \begin{aligned} &\|\mathbf{s}\| = 93\ &\theta = 220^\circ \end{aligned} $$ ## Calculate horizontal component Using the *Trigonometric Resolution* knowledge point $$ \begin{aligned} &a = 93 \cos(220^\circ)\ &a \approx 93 \times (-0.766044)\ &a \approx -71.2421 \approx -71.24 \end{aligned} $$ ## Calculate vertical component Using the *Trigonometric Resolution* knowledge point $$ \begin{aligned} &b = 93 \sin(220^\circ)\ &b \approx 93 \times (-0.642788)\ &b \approx -59.7792 \approx -59.78 \end{aligned} $$ ## Write vector in component form Using the *Vector Components* knowledge point $$ \mathbf{s} = -71.24\mathbf{i} - 59.78\mathbf{j} $$ Suppose the vector $\mathbf{s}$ has magnitude 93 and makes an angle of $220^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{s}$ is in standard position. Write $\mathbf{s}$ in the form $\mathbf{s} = a\mathbf{i} + b\mathbf{j}$. Do not round any intermediate computations, and round the values in your answer to the nearest hundredth. $\mathbf{s} =$ $-71.24\mathbf{i}-59.78\mathbf{j}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Vector Components" ] }

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Question

Explanation:

Identify vector parameters

Calculate horizontal component

Calculate vertical component

Write vector in component form

Answer: