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What are the x and y components of a vector a with arrow in the xy plane if its direction is 110° counterclockwise from the positive direction of the x axis and its magnitude is 8.7 m?

Am I supposed to solve by multiplying 8.7 and 110 and cos to get x? And then multiplying 8.7 and 110 and sin to get y?

user366783
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2 Answers2

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$$|R| = 8.7\ m$$

$$\theta = 110^{\circ}$$

The components are given by the simple formulas:

$$R_x = R\cdot\cos\theta$$

$$R_y = R\cdot\sin\theta$$

Enrico M.
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It's a fairly straight-forward solution once you draw a rough graph.

You'll see that the magnitude of the angle made to the $x$-axis can be found. Now that you have this, since length is a physical quantity, any sign convention will be the attribute of the direction it points to (i.e., $+x$-axis or $-x$-axis).

So, in this case, the angle made to the $-x$-axis, will be $70^{\circ}$. Now that you have this, treat the case normally.

The base (along the $-x$-axis) will be $8.7\cos(70^{\circ})$ and the height (along the $+y$-axis) will be $8.7\sin(70^{\circ})$.

Now that you have the magnitudes, a simple diagram will tell you that the base will be negative as it lies on the $-x$-axis and the height will be positive as it is along the $+y$-axis.

I hope this solves your problem!

Daniel Buck
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A_R
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  • Is this how the graph sketch should look? http://imgur.com/a/jwrIf – user366783 Sep 20 '16 at 12:43
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    Absolutely! Now that you know diagrammatically how the picture looks, solve for the magnitudes normally, and then manually add in the directions. – A_R Sep 20 '16 at 12:49