In analyzing the horizontal and vertical motion of projectiles launched at an angle, the formulas involve the use of both cosine and sine functions. Here's why:
1. **Horizontal Motion**: The horizontal component of the projectile's motion is affected by the cosine function. The horizontal distance traveled by the projectile can be calculated using the equation: \[ \text{Horizontal distance} = \text{Initial velocity} \times \text{time} \times \cos(\text{launch angle}) \]
2. **Vertical Motion**: The vertical component of the projectile's motion is affected by the sine function. The height or vertical displacement of the projectile at a certain time can be calculated using the equation: \[ \text{Vertical displacement} = (\text{Initial velocity} \times \sin(\text{launch angle}) \times \text{time}) - (0.5 \times \text{acceleration due to gravity} \times \text{time}^2) \]
By using both cosine and sine functions in these formulas, we can accurately analyze the horizontal and vertical motion of projectiles launched at an angle. It's important to consider both components to understand the complete trajectory of the projectile.
