Question

TRIGONOMETRY What are the horizontal and vertical components of this vector?

Answer 1

Since its angle is 35°, it is on the first quadrant, which means their components are positive.

Using a unit circle, we can remember that the x-axis corresponds to the cosine value and the y-axis to the sine value of the angle. The difference in thsi case is that we need to multiply the sine and cosine by the magnitute of the vector.

So, the x component will be using the magnitude and the cosine:

`\begin{gathered} x=50\cos 35\degree \\ x=50\cdot0.819152\ldots \\ x=40.9576\ldots \\ x\approx41.0 \end{gathered}`

And the y component will use the magnitude and the since:

`\begin{gathered} y=50\sin 35\degree \\ y=50\cdot0.573576\ldots \\ y=28.6788\ldots \\ y\approx29.7 \end{gathered}`

So, the components are approximately (41.0, 29.7)