Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 30°.
A)? $\langle 4 \sqrt { 3 } , 4 \rangle$
B)? $\langle 4,4 \sqrt { 3 } \rangle$
C)? $\langle 8,8 \sqrt { 3 } \rangle$
D)? $\langle 8 \sqrt { 3 } , 8 \rangle$
E)? $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question

Quizplus · Accepted Answer

The component form of a vector with magnitude $r$ and angle $\theta$ to the x-axis can be found using $r\cos(\theta)$ for the x-component and $r\sin(\theta)$ for the y-component. Given $r = 8$ and $\theta = 30°$, the x-component is $8\cos(30°) = 8(\sqrt{3}/2) = 4\sqrt{3}$ and the y-component is $8\sin(30°) = 8(1/2) = 4$, making the component form $\langle 4\sqrt{3}, 4 \rangle$.

Find the Component Form of V If ∥v∥=8\| \mathbf { v } \| = 8∥v∥=8

Find the Component Form of V If $\| \mathbf { v } \| = 8$