As Agent Trigonometry, you are given this clue:
Another way to solve a trig equation is to use factoring or the quadratic formula. Let’s look at a couple of examples.
This sine equation looks a lot like the quadratic
There is no solution for
To solve this equation, use the Pythagorean Identity
Solving each factor for
Solution: This equation is not factorable so you have to use the Quadratic Formula.
The first answer is within the range, but the second is not. To adjust -0.954 to be within the range, we need to find the answer in the second quadrant,
Concept Problem Revisit We can solve this problem by factoring.
Over the interval
Solve the following trig equations using any method in the interval
1. Put everything onto one side of the equation and factor out a cosine.
2. Recall that
3. This quadratic is not factorable, so use the quadratic formula.
The other solutions in the range are
Solve the following trig equations using any method. Find all solutions in the interval
Using your graphing calculator, graph the following equations and determine the points of intersection in the interval