Find the component form of the vector v with directional angle 115 and magnitude 6.

Question

Student’s Work Student’s Answer A. $\langle -1.84,4.68\rangle $ B $\langle -2.54,5.44\rangle $ C $\langle -3.28,6.04\rangle $ D $\langle 2.45,4.58\rangle $

Answer 1

To find the component form of the vector, we can use the following formulas based on the magnitude and directional angle:

Given magnitude: 6
Given directional angle: 115 degrees

Using the formulas:
v_x = |v| * cos(theta)
v_y = |v| * sin(theta)

Substitute the values:
v_x = 6 * cos(115 degrees) ≈ 6 * (-0.691) ≈ -4.145
v_y = 6 * sin(115 degrees) ≈ 6 * 0.723 ≈ 4.338

Therefore, the component form of the vector v is approximately $\langle -4.145, 4.338\rangle$.

So, the closest answer choice is A. $\langle -1.84,4.68\rangle$.