Question

the trigonometric functions are not one-to-one. but mathematicians wanted to define inverse functions. before that could be done, we first needed to restrict the domains of the original functions so that the functions became one-to-one on the new, smaller domains. what were those restricted domains?

Answer 1

The restricted domains for the inverse trigonometric functions are the quadrants, that can be each of the following intervals:

• 0 < x < 0.5π.

• 0.5π < x < π.

• π < x < 1.5π.

• 1.5π < x < 2.

What are equivalent angles?

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant. The relevance to these equivalent angles is that they may have equal values for the trigonometric functions, meaning that they are not one-to-one.

If we restrict the domain of the trigonometric functions in any of the four quadrants, we guarantee that they are one-to-one, hence the restricted domains are given as follows:

• 0 < x < 0.5π.

• 0.5π < x < π.

• π < x < 1.5π.

• 1.5π < x < 2.

More can be learned about trigonometric functions at brainly.com/question/16818112

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