Question

multiple choice question
if θ_y is the angle that force f forms with the y axis, then identify the expression for the horizontal component f_h of force f in space.
o f sin θ_y
o f cos θ_y
o -f cos θ_y
o -f sin θ_y

Explanation:

Step1: Recall force - component relationship

In a two - dimensional or three - dimensional space, if we consider the angle $\theta_y$ between the force $\vec{F}$ and the $y$ - axis, we can use trigonometric relations to find the components of the force.
The horizontal component of a vector (in a right - handed coordinate system) can be related to the magnitude of the vector and the angle with the $y$ - axis.
We know that if we consider the right - triangle formed by the force vector $\vec{F}$, its horizontal component $F_h$ and its vertical component, $\sin\theta_y=\frac{F_h}{F}$ (assuming the appropriate orientation of axes).

Step2: Solve for the horizontal component

From $\sin\theta_y=\frac{F_h}{F}$, we can isolate $F_h$ by multiplying both sides of the equation by $F$. So, $F_h = F\sin\theta_y$.

Answer:

A. $F\sin\theta_y$