In this video lesson we will discover how to Solve Trigonometric Equations using Inverses.
In our previous lesson, we learned all the tricks and techniques for solving all types of trigonometric equations using the Unit Circle.
Well, in this lesson, we are going to combine these same skills, but also use the power of Inverses and our calculators, to solve equations.
Remember, an inverse is something that can undo something else – it’s like an opposite, just like addition is the inverse of subtraction. And that’s the power of using Inverse Trig Functions, because they allow us to isolate our angle without having to use our Left Hand Trick.
More specifically, they’re the only way to solve equations when we aren’t given values readily found on the Unit Circle, as we will see in great detail when solving Oblique Triangles (i.e., Law of Sines and Cosines), and they will be of great importance when we look at displacement, force and velocity vectors.
Solving for the unknown angle using Inverses
But, there is a warning!
While Solving Equations using Inverse Trig Functions is awesome and easy, we have to remember that they will only give us one solution…. it’s up to us to determine if there are any more answers that will work for the given interval.
Huh?
Recall that Inverse Functions must pass the Horizontal Line Test, which means that we restrict the domain of our original function, which in-turn restricts the range of our inverse function. Consequently, this means we are only allowed to exist in specified quadrants… remember the “Bermuda Quadrant”?
Once we arrive at our desired answer we must either use Reference Angles to list all other possible solutions or make reference to possible Coterminal angles.
How to Solve Trig Equations Using Inverses – Video
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