A vector is a vector inclined and at an angle 'theta' to X-axis.write the formula for its X and Y components.
Answers
Explanation:
Thermodynamic equilibrium, condition or state of a thermodynamic system, the properties of which do not change with time and that can be changed to another condition only at the expense of effects on other systems.
First solve for the x and y components of vector A.
Let us call the magnitude of vector A as R. The x-component of R = cos θ * R. The y- component = sinθ * R.
To solve for the value of angle θ the formula is tan θ = (y-component of R) / (x-component of R). In symbols: tanθ = y-component / x-component To solve for angle θ use tanθ^-1 = y/x.
As a numerical example: Suppose vector A has a magnitude of 2 forming θ degrees with the positive x-axis.
x = 2 * cos θ and y = 2 * sin θ ; y/x = tan θ ; y/x = 2* sinθ / 2 cos θ ; tan θ = sinθ / cosθ
If θ = 30 degrees then y = 2 * sin 30 = 2 * 1/2 = 1; x = 2 * cos 30 degrees = 2 * 0.8660 which is simplified to x = 1.732.
tan θ = 1 / 1.1732 when simplified is 0.57737 and tan^-1 (0.57737) = 30.01 degrees due to rounding errors.