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What is the period of the function #y= -2 cos(4x-pi) -5#?

Answer 1

#pi/2#

In a sinusoidal equation

#y = a cos(bx+c) + d#,

the amplitude of the function will equal #|a|#, the period will equal #(2pi)/b#, the phase shift will equal #-c/b#, and the vertical shift will equal #d#.

So when #b = 4#, the period will be #pi/2# because #(2pi )/4 = pi/2#.

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Answer 2

Victoria Adebayo

The period of the function (y = -2\cos(4x-\pi) - 5) is given by (T = \frac{2\pi}{|b|}) in the general form (y = A\cos(bx - c) + D), where (b) is the coefficient of (x) in the cosine function.

In this case, the coefficient of (x) is 4, so (|b| = 4). Therefore, the period (T) is calculated as:

[ T = \frac{2\pi}{4} = \frac{\pi}{2} ]

So, the period of the function is (\frac{\pi}{2}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.