state the amplitude, period and phase shift of the function y=tan (20-80 degrees)
The function should read y = tan(2 theta - 180 degrees).
write it as
y = tan 2(Ø - 90°)
We don't speak of "amplitude" with tanØ (look at a graph of sinØ )
the period of tan kØ is 180/k°
in your case the period is 180/2 = 90°
the phase shift is 90° to the right.
To find the amplitude, period, and phase shift of the function y = tan(20 - 80°), let's break it down step by step.
1. Amplitude: The function y = tan(x) does not have a defined amplitude because it is an unbounded curve. The tangent function can take on values ranging from negative infinity to positive infinity.
2. Period: The period of the tangent function is π radians or 180 degrees, which means that the function repeats itself every 180 degrees or π radians.
3. Phase Shift: In the given function y = tan(20 - 80°), the angle inside the tangent function is (20 - 80°). Since the general form of the tangent function is y = tan(x - c), the phase shift, c, is equal to the angle inside the parentheses. In this case, the phase shift is equal to (20 - 80°).
So, to summarize:
- The amplitude of the function y = tan(20 - 80°) is not defined because the tangent function is unbounded.
- The period of the tangent function is π radians or 180 degrees.
- The phase shift of the function y = tan(20 - 80°) is (20 - 80°).