To calculate the vertical and horizontal components of a vector:
\[ Vc = M \cdot \sin(a) \]
\[ Hc = M \cdot \cos(a) \]
Where:
Vertical and horizontal components are the values of the base and height of a triangle formed with a vector as measured from the x-axis of a graph. In other words, when the horizontal and vertical components are put together to form a triangle, the resulting hypotenuse is the original vector.
Let's assume the following values:
Using the formulas:
Step 1: Convert the angle to radians:
\[ a = 30 \times \frac{\pi}{180} \approx 0.524 \text{ radians} \]
Step 2: Calculate the vertical component:
\[ Vc = 10 \times \sin(0.524) \approx 5 \]
Step 3: Calculate the horizontal component:
\[ Hc = 10 \times \cos(0.524) \approx 8.66 \]
Let's assume the following values:
Using the formulas:
Step 1: Convert the angle to radians:
\[ a = 45 \times \frac{\pi}{180} \approx 0.785 \text{ radians} \]
Step 2: Calculate the vertical component:
\[ Vc = 20 \times \sin(0.785) \approx 14.14 \]
Step 3: Calculate the horizontal component:
\[ Hc = 20 \times \cos(0.785) \approx 14.14 \]