Vector A⃗ , in the first quadrant, has a magnitude |A⃗ |= 1.0 and is at an angle α = 40 ∘ with respect to the positive x-axis. Vector B⃗ , in the fourth quadrant, has a magnitude |B⃗ |= 2.5 and is at an angle β = 20.0 ∘ with respect to the positive x-axis.
Find the x and y components of the vectors A⃗ and B⃗ . Notice that the answer box will accept and evaluate some mathematical functions. e.g. you can enter 5*sin(3.14/180*50) and the system will evaluate it as 5*sin(50 degrees). One important thing to notice is that the arguments for the trigonometric functions have to be in radians, not in degrees if you choose to use this feature.
Ax=
Ay=
Bx=
By=
ax= 1.5*sin(40)
ay=-1.5*cos(40)
bx=2.5*sin(20)
only bx is correct
ax = 1.5*sin(40)
ay = -1.5*cos(40)
bx = 2.5*sin(20)
by = -2.5*cos(20)
To find the x and y components of a vector, we can use the trigonometric functions sine and cosine.
For vector A⃗ , we have:
Magnitude |A⃗ | = 1.0
Angle α = 40 °
To find Ax (the x component of vector A⃗ ):
Ax = |A⃗ | * cos(α)
= 1.0 * cos(40°)
To find Ay (the y component of vector A⃗ ):
Ay = |A⃗ | * sin(α)
= 1.0 * sin(40°)
Similarly, for vector B⃗ , we have:
Magnitude |B⃗ | = 2.5
Angle β = 20.0 °
To find Bx (the x component of vector B⃗ ):
Bx = |B⃗ | * cos(β)
= 2.5 * cos(20°)
To find By (the y component of vector B⃗ ):
By = |B⃗ | * sin(β)
= 2.5 * sin(20°)
Now we can calculate the values:
Ax = 1.0 * cos(40°) ≈ 0.766
Ay = 1.0 * sin(40°) ≈ 0.643
Bx = 2.5 * cos(20°) ≈ 2.355
By = 2.5 * sin(20°) ≈ 0.847
Therefore, the x and y components of vectors A⃗ and B⃗ are approximately:
Ax ≈ 0.766
Ay ≈ 0.643
Bx ≈ 2.355
By ≈ 0.847