Solving for the X and Y components of a Vector

[slu1986]

1. A vector is 40.0 m long and makes an angle of 50.0° counterclockwise from the y-axis (on the side of the -x-axis). What are the x- and y-components of this vector?




2. Homework Equations
Sin = opp/hyp
Cos = adj/hyp


3. I tried solving for the x and y components of the vector by taking the -cos(50.0) 40.0m and came up with this= x-component: -25.7 and for the y component I took the sin (50.0) 40.0 m and came up with this = y-component: 30.6 m. However, these answers aren't correct and I don't understand what I am doing wrong. Could someone please explain exactly what I'm doing wrong.

 

[ideasrule]

Imagine the Cartesian grid, with its x- and y-axis stretching to infinity. Imagine an arrow going off at 50 degrees to the y-axis. Then, imagine a line going from the end of the arrow to the y-axis. Do you see why the x-component isn't -40cos(50)?

 

[slu1986]

I drew out the vector in the second quadrant which means the x component would be negative and the y component would be positive right? I'm sorry, but I do not understand what I'm doing wrong.

 

[ideasrule]

Note the right triangle in your drawing, formed by the vector, the y-axis, and the line from the end of the vector to the y-axis. The horizontal part--the leg from the y-axis to the vector--is the "opposite" side from the 50-degree angle, so its length would be 40sin(50). It also represents the distance from the x=0.

 

[slu1986]

I am still confused, I did what you're saying for the y-component. So the 40 sin(50) would be the x component? I thought only cosine could be used to find the x component and sin for the y component.