state the amplitude, period and phase shift of the function y = tan (2 theta- 180 degrees)
To determine the amplitude, period, and phase shift of the function y = tan (2θ - 180°), we need to rewrite the equation in a more recognizable format.
First, let's start by rewriting the equation to match the general form of the tangent function: y = tan (Bθ - C), where B and C are constants.
Given equation: y = tan (2θ - 180°)
Now, let's rewrite the given equation into the general form by isolating the terms:
y = tan (2θ - 180°)
y = tan (2(θ - 90°))
By comparing these equations, we can determine the values of B and C:
The general form is y = tan (Bθ - C).
From the equation y = tan (2(θ - 90°)), we can see that B = 2 and C = 180°.
Therefore, B = 2 and C = 180°.
Now, let's determine the amplitude, period, and phase shift:
1. Amplitude:
The tangent function does not have an amplitude. It can take any value between negative infinity and positive infinity.
2. Period:
To calculate the period of the function, we need to find the value of the constant B. In this case, B = 2.
The period of the tangent function is given by the formula: Period = π/B.
So, the period of the given function is Period = π/2.
3. Phase Shift:
To find the phase shift, we need to determine the value of C. In this case, C = 180°.
The phase shift of the tangent function is given by the formula: Phase Shift = C/B.
So, the phase shift of the given function is Phase Shift = 180°/2 = 90°.
In summary,
Amplitude: The tangent function does not have an amplitude.
Period: The period of the function is π/2.
Phase Shift: The phase shift of the function is 90°.
To determine the amplitude, period, and phase shift of the given function y = tan(2θ - 180°), we need to understand the properties of the tangent function and its transformations.
The amplitude of the tangent function is not defined since it has no upper or lower limit. Therefore, the amplitude for this function is undefined.
Next, let's analyze the period of the function. The period of the tangent function, denoted as T, is defined as the distance between two consecutive peaks or troughs of the graph. The general formula for the period of the tangent function is given by T = π/|B|, where B is the coefficient of θ.
In this case, the coefficient of θ is 2. So, the period (T) of the given function is T = π/|2| = π/2.
Now, let's determine the phase shift of the function. The phase shift is a horizontal translation of the graph, moving it left or right. It is given by the formula -C/B, where C is the constant term in the function and B is the coefficient of θ.
In our function, the coefficient of θ is 2 and there is no constant term. Therefore, the phase shift (P) of the given function is P = 0.
To summarize:
- Amplitude: Undefined
- Period: π/2
- Phase shift: 0