Question

For each other following sinusodial functions,determine its period in exact terms of pi.

(A) Y=6sin(10x)

(B) Y=-2cos(8x)

(C) Y=7sin(1/3x)

(D) Y=2/3cos(4/3x)

(E) Y=8sin(0.25x)

(F) Y=2.5cos(0.4x)
GL with that if Uk how to do it, I'm counting on u for a hw grade lmao

Answer 1

Answer:

Graphs of y = a sin x and y = a cos x

by M. Bourne

(a) The Sine Curve y = a sin t

We see sine curves in many naturally occuring phenomena, like water waves. When waves have more energy, they go up and down more vigorously. We say they have greater amplitude.

Let's investigate the shape of the curve y = a sin t and see what the concept of "amplitude" means.

Have a play with the following interactive.

Sine curve Interactive

You can change the circle radius (which changes the amplitude of the sine curve) using the slider.

The scale along the horizontal t-axis (and around the circle) is radians. Remember that π radians is \displaystyle{180}^{\circ}180

∘

, so in the graph, the value of \displaystyle\pi={3.14}π=3.14 on the t-axis represents \displaystyle{180}^{\circ}180

∘

and \displaystyle{2}\pi={6.28}2π=6.28 is equivalent to \displaystyle{360}^{\circ}360

∘

.