Find the period of 3tan1/2*x. Also explain me the graph of y=tanx with asymptote and the curves up and down,how they come in graph?
the period of tan(kx) is π/k
since tanx = sinx/cosx, there is an asymptote everywhere cosx = 0. That is at all odd multiples of π/2
What is asymptote and how is it related to sinx/cosx? Why tan graph from down to top in a curve way?
you really need to study your Algebra 2 some more if you don't understand asymptotes. google the topic and see what you can learn there.
Surely your trig book explains the graphs of the trigonometric functions.
In that case please help me as I have only the graph in my book which does not explain how it has been derived.
you can take a look at this link below:
h ttps://socratic.org/questions/how-do-you-graph-y-3tan-1-2x-2
there's no space between h and ttps
To find the period of the function 3tan(1/2*x), we first need to understand what the period of a function is.
The period of a function is the length of one complete cycle of the function's graph. In trigonometric functions like tangent (tan), the period is the length of one complete oscillation between two consecutive high or low points on the graph.
Now, let's find the period of the function 3tan(1/2*x):
1. The general form of the tangent function is y = A*tan(Bx), where A and B are constants.
2. In this case, A = 3 and B = 1/2.
3. The period of the tangent function is given by the formula P = (2π)/B. B = 1/2 in our case.
4. Substituting the value of B into the formula, we get P = (2π)/(1/2) = 4π.
Therefore, the period of the function 3tan(1/2*x) is 4π.
Now, let's discuss the graph of y = tan(x) to understand its behavior and the presence of asymptotes.
The graph of y = tan(x) has some distinct features:
1. Vertical Asymptotes: The function has vertical asymptotes at x = (π/2) + nπ and x = (3π/2) + nπ, where n is any integer. This means that the graph approaches positive or negative infinity as it gets closer to these values.
2. Periodicity and Symmetry: The graph repeats itself every π radians. It has a vertical line of symmetry at x = 0. The function tan(x) is an odd function, so it is symmetric about the origin (0,0), which means the graph is unchanged when reflected across the origin.
3. Curves Up and Down: In each period of tan(x), there are alternating curves that go up and down. The curve approaches positive infinity as it reaches the vertical asymptote on the right and negative infinity as it reaches the vertical asymptote on the left.
To visualize the graph of y = tan(x), you can plot points for various values of x or use a graphing tool to see the graph and its behavior.