What is the component form of vector v given a magnitude of 9 and an angle of theta= 90 degrees with positive x axis.
sorry I'm writing this on my phone and I don't have the symbols for vector, theta, or degree.
(0,9)
No problem! I can still help you with your question. To find the component form of a vector, we need to determine its x-component and y-component.
In this case, let's consider the vector v with a magnitude of 9 and an angle of 90 degrees with the positive x-axis.
To begin, we can convert the given angle from degrees to radians, as most mathematical functions use radians. Since 1 radian is equal to 180 degrees divided by π (pi), we can convert 90 degrees to radians using the formula:
angle in radians = (angle in degrees) * (π / 180).
By substituting the given angle of 90 degrees, we have:
angle in radians = 90 * (π / 180) = π / 2.
Now, we can use trigonometric functions (specifically cosine and sine) to find the x and y components respectively.
The x-component (v_x) can be found using the formula:
v_x = magnitude * cos(angle in radians).
Substituting the values we have:
v_x = 9 * cos(π / 2).
Since cos(π / 2) is equal to 0, we get:
v_x = 9 * 0 = 0.
Therefore, the x-component of vector v is 0.
Next, we can find the y-component (v_y) using the formula:
v_y = magnitude * sin(angle in radians).
Substituting the values we have:
v_y = 9 * sin(π / 2).
Since sin(π / 2) is equal to 1, we get:
v_y = 9 * 1 = 9.
Hence, the y-component of vector v is 9.
Therefore, the component form of vector v is (0, 9).