Use a graph of the cosecant function to find the value of theta for which csc theta equals 1.
-Go up to 1 on the vertical axis
-go horizontally until you cross or meet the graph
- read the corresponding value on the horizontal axis (should be π/2 or 90°)
To find the value of θ for which csc(θ) equals 1 using a graph of the cosecant function, follow these steps:
1. Understand the cosecant function: The cosecant function, csc(θ), is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ).
2. Graph the cosecant function: Plot the graph of the cosecant function on a coordinate plane. The graph will repeat its pattern every 2π radians or 360 degrees.
3. Locate the value of 1: Look for the y-value of 1 on the graph of the cosecant function.
4. Identify the corresponding angle: Once you locate the point where the graph intersects the y-value of 1, find the corresponding angle on the x-axis. This angle represents the value of θ for which csc(θ) equals 1.
Note: Since the cosecant function has vertical asymptotes at the zeros of the sine function, you will find multiple angles for which csc(θ) equals 1. These angles will be symmetrical about the x-axis.
Here is a sample graph of the cosecant function:
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-1 | 1
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-π 0 π 2π 3π 4π
From the graph, you can see that the graph of csc(θ) intersects y=1 at two points: θ=π/2 and θ=3π/2. Thus, those are the values of θ for which csc(θ) equals 1.