Finding Vector Components: Magnitude 15, Angle 315

[robfrech]

How do you find the components of this vector:

Magnitude 15, angle 315

Thanks!

 

[robfrech]

How do you find the components of this vector:

Magnitude 15, angle 315

Thanks!

 

[mathman]

Your question seems to imply a 2-d vector.

x=15cos(315)
y=15sin(315)

 

[tiny-tim]

Welcome to PF!

How do you find the components of this vector:

Magnitude 15, angle 315

Thanks!

Hi robfrech! Welcome to PF!

Draw a diagram, including the x and y axes.

Then use trigonometry to find the x and y coordinates … taking care to use a minus sign where appropriate!

 

[chroot]

Draw a picture and consider the resulting triangle. You know the length of the hypotenuse, and two of the angles. Use trigonometry to find the other sides.

- Warren

 

[joe215]

How do you draw a triangle with a 315 degree angle?

 

[HallsofIvy]

Well, first you should have specified where the angle is measured from!

The convention is that the angle is measured from the positive x-axis so I will assume that. Now 315= 360- 45 so you have a a point in the 4th quadrant with x-coordinate positive and y-coordinate negative. The triangle itself has hypotenuse 15, angle 45 degrees. x= 15 cos(45), y= -sin(45). Since cos(315)= cos(45) and sin(315)= -sin(45), that is exactly what mathman said originally.

 

[chroot]

Draw two crossed lines, representing the x and y axes. Draw a circle centered on the origin. Count 315 degrees around the circle, counterclockwise, starting from the point where the circle meets the positive x-axis. The point is in the lower-right quadrant. Draw two lines: one from the origin to the point, the other from the x-axis to the point. The second line should make a right angle with the x-axis.

You've now created a triangle. You know one angle and two sides. You can solve for the others.

- Warren