A pendulum is release data point 5 meters to the right of its position at rest. Graph a cosine function that represents the pendulum's horizontal displacement relative to its position at rest if it completes one back-and-forth swing every π seconds.

A 1.4-m pendulum is initially at its leftmost position of -9 degrees .Determine the period for one back-and-forth swing. Use g= 9.8 m/sec2 .Write a model for the angular displacement of the pendulum after t seconds.

Graph one complete period of the equation y = 2 sin (3x) + 5 . Label all key values on the axes, with the x-axis labeled in radians.

In whoville, the amount of rainfall varies greatly each week and follows a sinusoidal pattern. The following data is the recorded millimeters (mm) of precipitation across 14 weeks. Determine a sine and a cosine function that approximates the amount of rainfall over time in weeks. Decimals are allowed. Week 1, rainfall(mm) - 1.4 Week 2, rainfall(mm) - 3.1 Week 3, rainfall(mm) - 4.3 Week 4, rainfall(mm) - 2.9 Week 5, rainfall(mm) - 1.2 Week 6, rainfall(mm) - 0.1 Week 7, rainfall(mm) - 1.3 Week 8, rainfall(mm) - 2.7 Week 9, rainfall(mm) - 4.3 Week 10, rainfall(mm) - 3.2 Week 11, rainfall(mm) - 1.1 Week 12, rainfall(mm) - 0.2 Week 13, rainfall(mm) - 1.2 Week 14, rainfall(mm) - 2.8

Graph one complete cycle of y = y = 2 sin 2x- State the amplitude, period, and phase shift.

Please help find period, phase shift and vertical shift. Please graph, thank you!

what it means to have a change in amplitude and a change in period.

Consider an angle with an initial ray pointing in the 3-o'clock direction that measures 0 radians. The terminal point on a circle centered at the angle's vertex is h radius lengths to the right of the circle's center and v radius lengths above the circle's center. The slope of the terminal ray of the angle is m. Match each of the following inputs/outputs with their corresponding variable. (You can use each variable once, more than once, or not at all.) -1 The input of the cos function а. V The output of the cos - 1 function b. h The input of the sin - 1 function С. т d. 0 | The output of the sin- function 1 v The input of the tan function v The output of the tan' - 1 function

A swimmer on a floating air mattress will follow the rise and fall of the waves in lake. When the person is on the top of the wave her feet are 0.5m above the average surface height of the lake. When she is in a trough her feet dig 0.5m into the water (-0.5m). The peaks of the waves are separated by two seconds. Create an equation of the sinusoidal function that models this movement assuming that she starts at the average surface height of the lake and heads upwards.

An object moves in simple harmonic motion with period 8 seconds and amplitude 2 cm. At time t=0 seconds, its displacement d from rest is -2 cm, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time t.