What is the period of the trigonometric function y = 3\cos(4x)? — JAMB UTME

What is the period of the trigonometric function $y = 3\cos(4x)$ ?

The period of the given trigonometric function is

90^\circ

The period of a function of the form

y = a\cos(bx)

is given by

T = \frac{360^\circ}{b}

. Substituting

b = 4

yields

T = \frac{360^\circ}{4} = 90^\circ

Identify the standard form parameters

For

y = 3\cos(4x)

, amplitude

a = 3

and coefficient of

x

b = 4

The general form of a cosine function is

y = a\cos(bx + c) + d

Apply the period formula for trigonometric functions in degrees

Period

T = \frac{360^\circ}{b} = \frac{360^\circ}{4} = 90^\circ

The full cycle of a standard cosine graph completes in

360^\circ

, so multiplying the input by

b

compresses the period by a factor of

b

Period of a Cosine Function

Estimated Time:45s

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