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In your problem, ##\theta = 3x## runs from ##\theta = 0## to ##\theta = 3 \pi.## Look at a plot of ##y = \sin \theta## for ##0 \leq \theta \leq 3 \pi.## How many places are there at which ##\sin \theta = 1/2## or ##\theta = -1/2?##Physics53 said:
In trigonometry, an absolute value represents the distance of a number from zero on a number line. It is always positive and is typically denoted by two vertical lines around the number.
To solve absolute values in trigonometry, you must first identify the value inside the absolute value bars. Then, you can either take the positive or negative value, depending on the context of the problem. Finally, you can solve the equation as usual.
Some common techniques for solving absolute values in trigonometry include using the properties of absolute values, graphing the function, and using algebraic manipulation to isolate the absolute value expression.
Solving absolute values in trigonometry is important because it allows us to find the exact value of a function, rather than just its distance from zero. This is especially useful in real-world applications where finding precise measurements is necessary.
No, absolute values cannot be negative in trigonometry. As mentioned earlier, absolute values represent the distance from zero, which is always a positive value. However, when solving absolute values in an equation, the solution may be negative depending on the context of the problem.
