Equation b=a square ×cos square×2π×beta×Gama÷alpha
. The unit of a, alpha, beta are metre , 1/ sec and m/sec. Respectively the unit of b and gamma are
Use parentheses, cosine of what? Argument of cosine must come out unitless.
(1/alpha) cos^2(2p beta gamma) or cos^2(2pi beta gamma/alpha)
To determine the units of variables b and gamma in the given equation, we can examine each term separately and multiply their respective units together. Let's break down the equation:
b = a^2 × cos^2 × 2π × beta × Gama ÷ alpha
1. a^2:
Since the unit of a is meters (m), then a^2 would have the unit (m^2).
2. cos^2:
The cosine function does not have any units, so this term does not contribute to the overall units.
3. 2π:
The constant 2π represents the circumference of a circle and is dimensionless (without any units).
4. beta:
The unit of beta is m/sec.
5. Gama:
The unit of Gama is not specified, so we will assume it to be meters per second (m/sec).
6. alpha:
The unit of alpha is 1/sec.
Now, let's put it all together:
b = (m^2) × (m/sec)^2 × (dimensionless) × (m/sec) ÷ (1/sec)
Simplifying further:
b = (m^2) × (m^2/sec^2) × (m/sec) × sec
Combining like terms:
b = m^4/sec × m/sec
Finally:
b = m^5/sec^2
Therefore, the unit of b is meters to the power of 5 (m^5) divided by seconds squared (sec^2). The unit of gamma is not specified in the equation, so we cannot determine its unit without additional information.