Resolve the given vector into its​ x-component and​ y-component. The given angle thetaθ is measured counterclockwise from the positive​ x-axis (in standard​ position).
Magnitude 2.812.81 ​mN, thetaθequals=236.99236.99degrees° (round to the nearest hundredth as needed)

To resolve the given vector into its \( x \)-component and \( y \)-component, we'll use the following formulas:

\[
x = r \cdot \cos(\theta)
\]
\[
y = r \cdot \sin(\theta)
\]

Where:
- \( r = 2.81 \) mN (milliNewtons) is the magnitude of the vector,
- \( \theta = 236.99^\circ \) is the angle measured counterclockwise from the positive x-axis.

Now let's compute the \( x \)- and \( y \)-components.

\[
x = 2.81 \cdot \cos(236.99^\circ)
\]
\[
y = 2.81 \cdot \sin(236.99^\circ)
\]

I'll calculate these values.The \( x \)-component of the vector is approximately \( -1.53 \) mN, and the \( y \)-component is approximately \( -2.36 \) mN.

Would you like more details or have any further questions?

Here are 5 related questions to consider:
1. How do the signs of the components reflect the vector's direction in the coordinate plane?
2. How would the components change if the angle were different?
3. Can you express the vector in unit vector notation using \( \hat{i} \) and \( \hat{j} \)?
4. What would happen to the components if the magnitude were doubled?
5. How can you use the inverse tangent to find the angle from the components?

**Tip:** Always remember to convert angles to radians when using trigonometric functions in most programming languages!

Resolve the given vector into its x-component and y-component. The given angle θ is measured counterclockwise from the positive x-axis (in standard position). Magnitude 2.81 mN, θ = 236.99 degrees (round to the nearest hundredth as needed).

Learn how to resolve a vector into its x- and y-components using trigonometric functions. This problem involves a vector with magnitude 2.81 mN at an angle of 236.99 degrees, demonstrating key concepts in vector resolution and trigonometry. Suitable for Grades 10-12.

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