Final answer:
To calculate the average rate of change for the tangent function, choose two points on the curve, find the difference of the tangent values at these points, find the difference of the theta values, and then divide the first difference by the second.
Step-by-step explanation:
To calculate the average rate of change for the tangent function between two points using a calculator, you'll need to follow these steps:
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- Choose two points on the curve of the tangent function (tan(theta)). Let's call these points A(theta1, tan(theta1)) and B(theta2, tan(theta2)).
- Subtract the tan(theta) value at point B from the tan(theta) value at point A to find the change in the tangent function. This is the numerator in the average rate of change formula.
- Subtract theta1 from theta2 to find the change in theta. This is the denominator in the average rate of change formula.
- Divide the change in the tangent function by the change in theta to get the average rate of change.
- Mathematically, the average rate of change is expressed as
- Average Rate of Change
- = (tan(theta2) - tan(theta1)) / (theta2 - theta1)
- Make sure to use a calculator that is set to the correct mode (degrees or radians) corresponding to the values of theta you are using.