How does tanθ look like in a graph?
What would it be their y values?
To understand how tan(θ) looks like in a graph, let's first recall that tan(θ) is defined as the ratio of the sine (sin) of an angle (θ) to the cosine (cos) of that angle. In a graph, the angle θ is typically represented on the x-axis, while the value of tan(θ) is shown on the y-axis.
The graph of the tangent function, tan(θ), is periodic and repeats itself every π radians (180 degrees). It has asymptotes at odd multiples of π/2 radians (or 90 degrees), which means that the graph approaches positive or negative infinity as it gets closer to these points.
The y-values of tan(θ) can vary from negative infinity to positive infinity as θ increases or decreases. The graph will have positive y-values for angles in the first and third quadrants, while negative y-values will be present in the second and fourth quadrants. The function oscillates between positive and negative values as θ changes.
It is important to note that the graph of tan(θ) exhibits vertical asymptotes at θ = (2n + 1)π/2, where n is an integer. These vertical asymptotes correspond to the points where tan(θ) is undefined.
To visualize the graph of tan(θ) more accurately, it is recommended to use graphing software or online tools that can plot functions accurately based on the provided input.