In order to have an inverse, a function must be one-to-one, which means that its

Question

In order to have an inverse, a function must be one-to-one, which means that its graph must pass the Horizontal Line Test. If a function is not one-to-one, it is usually possibly to restrict its domain to make it one-to-one. Looking at the graphs of sine, cosine, and tangent, are they one-to-one? ___ In order to have inverse trig functions, we must restrict the domains of the functions to make them one-to-one. We will do this as follows: for sin (x), restrict the domain to -pi/2 lessthanorequalto x lessthanorequalto pi/2, and for tan (x), restrict the domain to -pi/2

Explanation / Answer

Please fill the given blanks in the following order:

No : Because all three graphs fail the horizontal line test.

Quadrants I and IV : (-pi/2, 0) is in forth quadrant and (0,pi/2) is in first quadrant.

Quadrants I and II : (0,pi/2) is in first quadrant and (pi/2, pi) is in second quadrant.

Range: We know that domain of original function is same as range of inverse function.

Angle: We know that the input to a trigonometric function is always an angle. In the same way, output to an inverse trigonometric function is too always an angle.

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