Explanation:

The domain the the tangent role does not include any kind of values of x that are odd multiples of π/2 .

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The selection of the sine function is native <-1, 1>.

The period of the tangent role is π, vice versa, the period for both sine and also cosine is 2π.

Which of the complying with represents a sine wave v a selection of ?    Explanation:

The selection of a sine wave is changed by the coefficient inserted in front of the basic equation. So, if friend have , this method that the highest suggest on the wave will be at and the shortest at . However, if friend then begin to transition the equation vertically by including values, together in, , climate you must account for said shift. This would certainly make the minimum value to be and the maximum worth to be . Because that our question, then, the is fine come use . The for the duty parameter only transforms the period of the equation, do its waves "thinner."

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### Example question #63 : Trigonometry

Which the the adhering to sine waves has actually a variety of to ? Explanation:

The variety of a sine wave is altered by the coefficient placed in prior of the basic equation. So, if friend have , this means that the highest suggest on the wave will certainly be at and the shortest at ; however, if friend then start to change the equation vertically by adding values, together in, , climate you should account for said shift. This would make the minimum worth to be and the maximum worth to be .

For ours question, the variety of values covers . This variety is achieved by having either or  merely flips the equation end the -axis. The range "spread" remains the same.) We should make the top value to it is in  . To carry out this, you will must add to . This requires an upward shift of . An instance of performing a shift like this is: Among the possible answers, the one that functions is: The parameter does no matter, together it only alters the frequency the the function.

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### Example question #64 : Trigonometry

What is the variety of the trigonometric function given by the equation:  Explanation:

The range of the sine and cosine features are the close up door interval indigenous the negative amplitude and also the confident amplitude. The amplitude is provided by the coefficient, in the adhering to general equation: . For this reason we view the range is: Report one Error

### Example question #65 : Trigonometry

What is the variety of the complying with trigonometric equation: ? Explanation:

The selection of a sine or cosine duty spans indigenous the negative amplitude come the positive amplitude. The amplitude is in the basic formula: Thus we see amplitude that our role is and so the selection is: Report an Error
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