Writing the Equation of a Periodic Wave from a Graph

  • 1.

    Work out the equation of the periodic wave given in the image.

    Periodic_wave_graph_2 sin ( 3x - pi)

    Answers:

    • {eq}y = 2 \sin ( 3x - 2 \pi) +1 {/eq}

    • {eq}y = 2 \sin ( 3x - \pi) {/eq}

    • {eq}y = 2 \sin ( 3x + \pi) +3 {/eq}

    • {eq}y = 2 \sin ( 3x - 5 \pi) -4 {/eq}

  • 2.

    Four options are given. Which one gives the correct equation of the wave shown here?

    Periodic_wave_graph_2cos(3x - 2 pi)

    Answers:

    • {eq}y = 2 \cos (3x) {/eq}

    • {eq}y = 2 \sin ( 3x - \pi) + 10 {/eq}

    • {eq}y = 2 \sin ( 3x -2) -5 {/eq}

    • {eq}y = 2 \sin ( 3x - 4 \pi) + 3 {/eq}

  • 3.

    Choose the correct equation of the periodic wave shown in the graph.

    Periodic_wave_graph_sin (3 pi - x) +1

    Answers:

    • {eq}y = \sin (3 \pi + x) -2 {/eq}

    • {eq}y = \sin (3 - x) +5 {/eq}

    • {eq}y = \sin (x) +1 {/eq}

    • {eq}y = \sin (3 \pi - 2x) -4 {/eq}

  • 4.

    What is the correct equation of the periodic wave shown in the figure?

    Periodic_wave_graph_2 sin (pi - 3x) +3

    Answers:

    • {eq}y = 2 \sin (2 \pi - 3x) +1 {/eq}

    • {eq}y = 2 \sin (3x +2 \pi ) - 3 {/eq}

    • {eq}y = 2 \sin (3x) +3 {/eq}

    • {eq}y = 2 \sin (3x + \pi) {/eq}

  • 5.

    Consider the image given below and tick the correct equation of the periodic wave displayed.

    Periodic_wave_graph_6 cos (pi - x)

    Answers:

    • {eq}y = 6 \cos (3 \pi - x) +1 {/eq}

    • {eq}y = 6 \cos(x-\pi) {/eq}

    • {eq}y = 6 \cos (2 \pi - x) {/eq}

    • {eq}y = 6 \cos (\pi - x) +4 {/eq}

  • 6.

    Study the graph of the given periodic wave shown below and find out its equation.

    Periodic_wave_graph_3  cos (x + 2 pi )

    Answers:

    • {eq}y = 5 \sin (x - \pi ) +1 {/eq}

    • {eq}y = 3 \cos (x) {/eq}

    • {eq}y = 4 \cos ( x - 2 \pi ) {/eq}

    • {eq}y = 2 \cos (2x - \pi ) +4 {/eq}

  • 7.

    As per the given graph, what is the equation of the periodic wave?

    Periodic_wave_graph_3 sin left (x + dfrac {3 pi}{5} right )

    Answers:

    • {eq}3 \sin \left (x-\frac{7\pi}{5} \right) {/eq}

    • {eq}2 \sin \left (x - \dfrac {3 \pi}{2} \right ) {/eq}

    • {eq}3 \sin \left (x + \dfrac {3 \pi}{2} \right ) +1 {/eq}

    • {eq}3 \sin \left (x + \dfrac {3 \pi}{4}\right ) +3 {/eq}

  • 8.

    Out of the given options, select the one that represents the correct equation of the periodic wave displayed here.

    Periodic_wave_graph_-3  cos (pi + x) + 1

    Answers:

    • {eq}3 \cos(x) + 1 {/eq}

    • {eq}-3 \sin (\pi + x) + 4 {/eq}

    • {eq}3 \cos (2 \pi + x) + 2 {/eq}

    • {eq}3 \sin (\pi + x) -4 {/eq}

  • 9.

    The result of an experiment is in the form of the periodic wave shown below. Determine the equation of the wave.

    Periodic_wave_graph_cos left ( dfrac {x}{2} + pi right)

    Answers:

    • {eq}h(x) = \cos \left ( \dfrac {x}{2} - \pi \right) {/eq}

    • {eq}h(x) = 2 \cos \left ( \dfrac {x}{2} - \pi \right) {/eq}

    • {eq}h(x) = \sin \left ( \dfrac {x}{2} + 3 \pi \right) {/eq}

    • {eq}h(x) =2 \sin \left ( \dfrac {x}{2} - \pi \right) {/eq}

  • 10.

    Select the correct equation of the periodic wave.

    Periodic_wave_graph_-2 sin left ( x+dfrac {3 pi }{2} right )

    Answers:

    • {eq}g(x) = 2 \sin\left(x-\frac{3\pi}{2}\right) {/eq}

    • {eq}g(x) = 2 \sin \left ( x+\dfrac {3 \pi }{2} \right ) +3 {/eq}

    • {eq}g(x) = -2 \cos \left ( 2 x+\dfrac {3 \pi }{2} \right ) {/eq}

    • {eq}g(x) = -2 \sin \left ( x+\dfrac {3 \pi }{2} \right ) +1 {/eq}

  • 11.

    Observe the image given below, and figure out the equation of the periodic wave.

    Periodic_wave_graph_cos ( x +pi) + 3.5

    Answers:

    • {eq}y = - \cos ( x +\pi) - 3.5 {/eq}

    • {eq}y = - \sin ( 2x +\pi) + 3.5 {/eq}

    • {eq}y = \cos(x-\pi)+3.5 {/eq}

    • {eq}y = \cos ( 2x -\pi) - 3.5 {/eq}

  • 12.

    What is the equation of periodic wave shown in the image?

    Periodic_wave_graph_4 sin( 2 pi +3x) - 2.5

    Answers:

    • {eq}f(x) = -4 \sin( \pi +3x) - 2.5 {/eq}

    • {eq}f(x) = 4 \sin(3x)-2.5 {/eq}

    • {eq}f(x) = 2 \cos ( \pi +3x) + 2.5 {/eq}

    • {eq}f(x) = -2 \sin( 2 \pi - 3x) + 2.5 {/eq}

  • 13.

    Pick out the option with the correct equation of the periodic wave displayed in the graph.

    Periodic_wave_graph_pi sin (4x + 2) + dfrac {pi}{2}

    Answers:

    • {eq}y = \pi \sin (x +1) - \dfrac {\pi}{2} {/eq}

    • {eq}y = - \pi \cos (4x ) + \dfrac {\pi}{2} {/eq}

    • {eq}y = \pi \sin(\frac{4\pi}{3}x+\frac{2\pi}{3})+\frac{\pi}{2} {/eq}

    • {eq}y = - \pi \sin (4x ) - \dfrac {\pi}{2} {/eq}

  • 14.

    Observe the graph and choose the correct option with the equation of the periodic wave.

    Periodic_wave_graph_2 sin left ( x + 5 pi 
ight ) - 1

    Answers:

    • {eq}y = 2 \sin(x-\pi)-1 {/eq}

    • {eq}y = -4 \cos \left ( x - 5 \pi \right ) - 1 {/eq}

    • {eq}y = 2 \cos \left ( x + \pi \right ) + 3 {/eq}

    • {eq}y = -2 \sin \left ( x + \pi \right ) +1 {/eq}

  • 15.

    Which of the following is the correct equation of periodic equation?

    Periodic_wave_graph_sin left (dfrac {4 pi}{3} + x 
ight ) +1

    Answers:

    • {eq}h(x) = \sin\left(x-\frac{3\pi}{4}\right)+1 {/eq}

    • {eq}h(x) = -2 \cos \left (\dfrac {4 \pi}{3} - x \right ) -2 {/eq}

    • {eq}h(x) = \cos \left (\dfrac { \pi}{3} + x \right ) - 2 {/eq}

    • {eq}h(x) =-2 \sin \left (\dfrac { \pi}{3} + x \right ) +1 {/eq}

  • 16.

    Determine the equation of the periodic wave as shown in the graph below.

    Answers:

    • {eq}f(x) = \sin \left ( \dfrac{\pi x}{2} \right ) + 1 {/eq}

    • {eq}f(x) = \sin \left ( \dfrac{\pi }{2} \right ) + 1 {/eq}

    • {eq}f(x) = \sin \left ( \dfrac{\pi x}{2} \right ) + 2 {/eq}

    • {eq}f(x) = \sin \left ( \dfrac{\pi x}{2} \right ) -1 {/eq}

  • 17.

    Use the graph below to determine the correct equation of the periodic function.

    Answers:

    • {eq}f(x) = \sin \left ( x+ \pi \right ) + 2 {/eq}

    • {eq}f(x) = \sin \left ( x+ \pi \right ) + 3 {/eq}

    • {eq}f(x) = \sin \left ( x+ \pi \right ) - 3 {/eq}

    • {eq}f(x) = \sin \left ( x- \pi \right ) - 3 {/eq}

  • 18.

    Which of the following option is the correct equation of the periodic wave as shown in the graph?

    Answers:

    • {eq}\sin (2 x) -1 {/eq}

    • {eq}\sin (x) -1 {/eq}

    • {eq}\sin (x) +1 {/eq}

    • {eq}\sin (x) -2 {/eq}

  • 19.

    Use the graph below to determine the correct equation of the periodic function.

    Answers:

    • {eq}\cos(x+2 \pi) +1 {/eq}

    • {eq}\cos(x-2 \pi) -1 {/eq}

    • {eq}\cos(2x+2 \pi) -1 {/eq}

    • {eq}\cos(x+2 \pi) -1 {/eq}

  • 20.

    Choose the correct option. By using the graph below, determine the equation of the periodic wave.

    Answers:

    • {eq}\cos(x - \pi) +2 {/eq}

    • {eq}2\cos(x + 2\pi) -2 {/eq}

    • {eq}\cos(x - 2 \pi) +2 {/eq}

    • {eq}\cos(x - \pi) -2 {/eq}

  • 21.

    Which of the following option is the correct equation of the periodic wave as shown in the graph?

    Answers:

    • {eq}2 \cos(-x - \pi ) {/eq}

    • {eq}\cos(2x) {/eq}

    • {eq}2 \cos(2x +3 \pi) {/eq}

    • {eq}2 \cos(2x -\pi) {/eq}

  • 22.

    Determine the equation of the periodic wave as shown in the graph below.

    Answers:

    • {eq}2 \sin \left (x - \dfrac{\pi}{2} \right ) - \pi {/eq}

    • {eq}2 \sin \left (x - \dfrac{\pi}{2} \right ) - 2 \pi {/eq}

    • {eq}2 \sin \left (x - \dfrac{\pi}{2} \right ) + 2 \pi {/eq}

    • {eq}2 \sin \left (x - \dfrac{\pi}{2} \right ) + \pi {/eq}

  • 23.

    Use the graph below to determine the correct equation of the periodic function.

    Answers:

    • {eq}g(x) = \sin \left ( x + \dfrac{3 \pi }{2} \right ) - 0.5 {/eq}

    • {eq}g(x) = \sin \left ( x + \dfrac{3 \pi }{2} \right ) + 1.5 {/eq}

    • {eq}g(x) = \sin \left ( x + \dfrac{3 \pi }{2} \right ) - 1.5 {/eq}

    • {eq}g(x) = \sin \left ( x + \dfrac{3 \pi }{2} \right ) + 0.5 {/eq}

  • 24.

    Which of the following option is the correct equation of the periodic wave as shown in the graph?

    Answers:

    • {eq}\sin ( 3x - \pi / 2 ) + 1 {/eq}

    • {eq}\sin ( 2 \pi - 3x) + 1 {/eq}

    • {eq}\sin ( \pi - 3x) - 1 {/eq}

    • {eq}\sin ( \pi / 2 - 2x) + 1 {/eq}

  • 25.

    Choose the correct option. By using the graph below, determine the equation of the periodic wave.

    Answers:

    • {eq}\dfrac 12 \cos (\pi -x) + 2 {/eq}

    • {eq}\dfrac 12 \cos (\pi + 2x) + 2 {/eq}

    • {eq}\dfrac 12 \cos (\pi -x) - 2 {/eq}

    • {eq}\dfrac 12 \cos (2 \pi -x) + 2 {/eq}

  • 26.

    Find the correct option that gives the equation of the periodic function using the graph below.

    Answers:

    • {eq}0.2 \sin (x+3 \pi) {/eq}

    • {eq}0.4 \sin (x+2 \pi) {/eq}

    • {eq}0.2 \sin (x - 2 \pi) {/eq}

    • {eq}0.4 \sin (x+ \pi) {/eq}

  • 27.

    Determine the equation of the periodic wave as shown in the graph below.

    Answers:

    • {eq}2 \cos \left ( \pi - \dfrac x2 \right ) {/eq}

    • {eq}3 \cos \left ( \pi - \dfrac x4 \right ) {/eq}

    • {eq}3 \cos \left ( \pi + \dfrac x4 \right ) {/eq}

    • {eq}3 \cos \left ( \pi - \dfrac x2 \right ) {/eq}

  • 28.

    Choose the correct option. By using the graph below, determine the equation of the periodic wave.

    Answers:

    • {eq}\sin (2 \pi - x) - 1 {/eq}

    • {eq}\sin ( \pi - x) + 2 {/eq}

    • {eq}\sin (2 \pi - 3x) + 1 {/eq}

    • {eq}\sin (\pi - x) + 1 {/eq}

  • 29.

    Use the graph below to determine the correct equation of the periodic function.

    Answers:

    • {eq}\cos \left ( \dfrac{\pi x}{4} \right ) {/eq}

    • {eq}\cos \left ( \dfrac{\pi x}{2} \right ) {/eq}

    • {eq}\sin \left ( \dfrac{\pi x}{2} \right ) {/eq}

    • {eq}\sin \left ( \dfrac{\pi x}{4} \right ) {/eq}

  • 30.

    Determine the equation of the periodic wave as shown in the graph below.

    Answers:

    • {eq}\cos(2x) + 2 \pi {/eq}

    • {eq}\cos(2x) + \pi {/eq}

    • {eq}\cos(x) + \pi {/eq}

    • {eq}\cos(2x) - \pi {/eq}

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