Find x and y components of a vector which is 10 units in length and 40 degrees below the +x axis.
I honestly don't even know how to begin this problem .. Please help me !
did you try drawing the figure? You just wind up with a right triangle, where one angle is 40° and the hypotenuse is 10.
x = 10 cos40°
y = -10 sin40°
Looks like time to review your trigonometry.
To find the x and y components of a vector, we can use trigonometry. Let's call the length of the vector "r" and the angle it forms below the +x axis "θ". In this case, r = 10 units and θ = 40 degrees.
To find the x component of the vector (x'), we use the cosine function:
x' = r * cos(θ)
Substituting the values we have:
x' = 10 * cos(40)
Now we can calculate the x' component of the vector:
x' ≈ 7.65 units
To find the y component of the vector (y'), we use the sine function:
y' = r * sin(θ)
Substituting the values we have:
y' = 10 * sin(40)
Now we can calculate the y' component of the vector:
y' ≈ -6.42 units
Therefore, the x and y components of the vector, which is 10 units in length and 40 degrees below the +x axis, are approximately 7.65 units in the x direction and -6.42 units in the y direction.