suppose the vector $\mathbf{t}$ has magnitude 78 and makes an angle of $304^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{t}$ is in standard position.

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

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

$\mathbf{t} = \square$

Question

suppose the vector $\mathbf{t}$ has magnitude 78 and makes an angle of $304^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{t}$ is in standard position.

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

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

$\mathbf{t} = \square$

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" ] } ## Identify the given parameters Using the *Vector Components* knowledge point $$ \begin{aligned} &\|\mathbf{t}\| = 78\ &\theta = 304^\circ \end{aligned} $$ ## Calculate the horizontal component Using the *Trigonometric Resolution* knowledge point $$ \begin{aligned} &a = 78 \cos(304^\circ)\ &a \approx 43.6179 \approx 43.62 \end{aligned} $$ ## Calculate the vertical component Using the *Trigonometric Resolution* knowledge point $$ \begin{aligned} &b = 78 \sin(304^\circ)\ &b \approx -64.6637 \approx -64.66 \end{aligned} $$ ## Write the vector in component form Using the *Vector Components* knowledge point $$ \mathbf{t} = 43.62\mathbf{i} - 64.66\mathbf{j} $$ Suppose the vector $\mathbf{t}$ has magnitude 78 and makes an angle of $304^\circ$ with the positive $x$-axis (measured counterclockwise), when $\mathbf{t}$ is in standard position. Write $\mathbf{t}$ in the form $\mathbf{t} = a\mathbf{i} + b\mathbf{j}$. Do not round any intermediate computations, and round the values in your answer to the nearest hundredth. $\mathbf{t} =$ $43.62\mathbf{i}-64.66\mathbf{j}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Vector Components" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the horizontal component

Calculate the vertical component

Write the vector in component form

Answer: