A vector has a magnitude of $5$ units and points $37°$ above the positive x-axis. What is the component form of this vector?

• A. $5,0$
• B. $3,4$
• C. $4,3$
• D. $0,5$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the vector has a magnitude of 5 units and makes an angle of 37\degree above the positive x-axis.
2. Recall that the component form of a vector \( \vec{v} \) with magnitude \( r \) and angle \( \theta \) is given by \( \vec{v} = (r \cos \theta, r \sin \theta) \).
3. Calculate the x-component by multiplying the magnitude by the cosine of the angle: \( x = 5 \times \cos 37\degree \).
4. Calculate the y-component by multiplying the magnitude by the sine of the angle: \( y = 5 \times \sin 37\degree \).
5. Write the component form of the vector as \( (x, y) \), using the values found in the previous steps.