ITF - Solving Equations with Technology Lesson

Solving Equations with Technology

You may be asked to solve an equation when the values given are not from the Unit Circle. When that happens, you may use your calculator! For this course, we will utilize degree mode on our calculator.

Watch this video to try 2 problems:

Try these problems to see if you've got it.

Find all angles equation image indicator $LaTeX: 0\le\theta\le360^\circ$ $0\le\theta\le360^\circ$ that satisfy the equations below:

The function below models the average monthly temperatures in Asheville, NC where t =0 represents January.

equation image indicator $LaTeX: f\left(t\right)=-18.5\cos\left(30t\right)+54.5$ $f\left(t\right)=-18.5\cos\left(30t\right)+54.5$

Use this function to find out about which months have an average temperature of equation image indicator LaTeX: 70° $70°$ .

1. Set the function equal to 70 and isolate the trig ratio:

equation image indicator $LaTeX: f\left(t\right)=-18.5\cos\left(30t\right)+54.5\\ 15.5=-18.5\cos\left(30t\right)\\ -0.83783=\cos\left(30t\right)$ $f\left(t\right)=-18.5\cos\left(30t\right)+54.5\\ 15.5=-18.5\cos\left(30t\right)\\ -0.83783=\cos\left(30t\right)$

2. Let U = 30t and rewrite the equation as: equation image indicator LaTeX: U=-0.83783 $U=-0.83783$ .

3. Solve this using the method you learned above:

equation image indicator $LaTeX: U=-0.83783\\ U=146.91°\\ U=213.09°$ $U=-0.83783\\ U=146.91°\\ U=213.09°$

4. Now, we can substitute for U in this equation: U = 30t (we have to do it twice!):

equation image indicator $LaTeX: 146.91=30t\\ 4.897=t\\ 5\approx t\\ or\\ 213.09=30t\\ 7.103=t\\ 7\approx t$ $146.91=30t\\ 4.897=t\\ 5\approx t\\ or\\ 213.09=30t\\ 7.103=t\\ 7\approx t$

So, in months 5 and 7 or June and August - Asheville has an average temperature of 70°.

You Try: Using the same function from above, determine the months in which 60 degrees is the average temperature.

Solution: May or September

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