Magnitude and Direction

You always want to make sure the trig function you are using is appropriate for the angle you are working with.In summary, when finding the x and y components of vectors, it is important to use the correct trig functions for the given angle. In this case, either angle (75* or 15*) could be used, but the appropriate trig functions must be applied to each angle to accurately find the components.
  • #1
Rich52490
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  • #2
Start out by finding the x and y components of the two vectors shown.
 
  • #3
F1 = 120cos(60*) = 60
120sin(60*) = 103.9
x and y = (60,103.9)

F2 = -75cos(75*) or is it -75cos(15*)? = -19 or -72.4
75sin(75*) or 75sin(15*) = 72.4 or 19
x and y = (-19,72.4) or is is it (-72.4, 19)
 
  • #4
Rich52490 said:
F1 = 120cos(60*) = 60
120sin(60*) = 103.9
x and y = (60,103.9)

F2 = -75cos(75*) or is it -75cos(15*)? = -19 or -72.4
75sin(75*) or 75sin(15*) = 72.4 or 19
x and y = (-19,72.4) or is is it (-72.4, 19)
Either angle (75* or 15*) would work, the problem arises when you apply the trig functions to find the components. For example, look at how the the cosine function is defined: cos(theta) = adj/hyp. In your second answer for the x component of F2, you are saying that the leg adjacent to the angle is on the x axis, when in reality it is along the y-axis according to the definition of cosine.
 

1. What is magnitude and direction?

Magnitude and direction are two components that describe a vector quantity. Magnitude refers to the size or amount of the vector, while direction refers to the orientation or angle of the vector.

2. How are magnitude and direction represented?

Magnitude is typically represented by a number and a unit, such as 10 meters or 5 seconds. Direction is often represented by an arrow pointing in the direction of the vector, or by an angle measured from a reference direction.

3. How are magnitude and direction related?

Magnitude and direction are closely related and cannot exist without each other. They are both necessary to fully describe a vector quantity. Changing either the magnitude or direction will result in a different vector.

4. Can the magnitude of a vector be negative?

Yes, the magnitude of a vector can be negative. This occurs when the vector is pointing in the opposite direction of the reference direction. For example, a displacement of -5 meters means that the object has moved 5 meters in the negative direction.

5. How are magnitude and direction measured or calculated?

Magnitude can be measured directly using a ruler or other measuring tool. It can also be calculated using mathematical equations, such as the Pythagorean theorem for finding the magnitude of a 2-dimensional vector. Direction can be measured using a protractor or calculated using trigonometric functions, such as tangent or sine.

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