A sine function is given by the equation y = 5\sin\left(\frac{2}{3}x\right) - 2. What is t… — JAMB UTME

A sine function is given by the equation $y = 5\sin\left(\frac{2}{3}x\right) - 2$ . What is the period of this trigonometric function in degrees?

Cevap: 540 degrees

The period of the trigonometric function is

540^\circ

For a general sine curve of the form

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

, the period

T

in degrees is calculated as

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

. Given

y = 5\sin\left(\frac{2}{3}x\right) - 2

, the value of

b

\frac{2}{3}

. Dividing

360^\circ

\frac{2}{3}

gives

540^\circ

Identify the coefficient

b

x

from the standard sine form

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

b = \frac{2}{3}

The coefficient of

x

determines the angular frequency and affects the horizontal compression or stretch of the graph.

State the period formula in degrees for a sine function.

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

The standard sine function completes one full wavelength over

360^\circ

, so scaling the input by

b

changes the period to

\frac{360^\circ}{b}

Substitute

b = \frac{2}{3}

into the formula and evaluate.

T = \frac{360^\circ}{\frac{2}{3}} = 360^\circ \times \frac{3}{2} = 540^\circ

Dividing by a fraction is performed by multiplying by its reciprocal.

Period of Trigonometric Functions

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