7. The number of visible sun spots varies rhythmically from 10 to 110 per year over a period of eleven years. The 110 max last occurred in the year 2014. Write a sinusoidal function N (t) to model that number of sun spots per year, where t is in years past the year 2014. What number of sun spots does your function predict for the year 2018? a.) b.)

Shown is your author’s chart,beginning January 25, 2015, when he was 25,473 days old. We all have cycles with the same amplitudes and periods as thoseshown here. Each of our three basic cycles begins at birth.The longer tickmarks correspond to the dates shown. Use the biorhythm chart shown to solve:If you extend these sinusoidal graphs to the end of the year, is there a day when your author should not even bother getting out of bed?

At its highest point, the second hand on a clock is 1.9 m above the ground. At its lowest point, the second hand is 1.6 m above the ground. The second hand starts at its highest point when the clock is started. a) Determine the function for the height of the second hand with respect to the number of seconds that have passed since the clock was started. [Hint: the second hand takes 60 seconds to complete one full rotation .] b) Determine the height of the hand at 10 s and 35 s. [Answers in degrees].

A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 20 seconds, and the average height of the bottle is 10 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height. Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? Part C: Based on the graph of the function, after how many seconds will it reach its lowest height?

On 31 January, 2009, during a heat wave in Mildura, Victoria, the maximum temperature recordedwas approximately 44 ◦C and the minimum overnight temperature recorded was approximately 26 ◦C. (a) Using a sine function, write down an equation that models the temperature T (in ◦C) in Mildura on that day as a function of t (measured in hours since midnight). Explain how you determine each of the constants in your equation, and write down any assumptions you make.

A light is placed on the tip of a windmill blade to protect planes from crashing into them. The windmill's center is 400 ft above the ground and the blades of the windmill are 180 feet long. The windmill rotates in the counter-clockwise direction and completes one full revolution every 10 seconds starting from the 3 o'clcok position. Define the function f that represents the light's distance above the ground in terms of the amount of time in seconds, t, since the windmill started rotating. Determine the equation of the midline for the function f. Graph the function using Desmos to check your answer. Assume y=f(t). Determine the amplitude of the function f. Graph the function using Desmos to check your answer.\ Determine the period of the function f. Graph the function using Desmos to check your answer.

Graph two full periods of the function f(x)=cos(2x) and state the amplitude and period. Amplitude A = period P =

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

In the theory of biorhythms, sine functions are used to measure a person's potential. Shown below is a person's chart beginning June 11. Everyone has cycles with the same amplitudes and periods as shown below. Each of the three cycles begins at birth. For the period shown, what is the best day in August for the person to meet an online friend for the first time? Emotional Plus Zero Minus -1- Physical Intellectual I M 6/16 6/11 6/21 6/26 The best day would be August (Type a whole number.) 111 7/11 7/6 ↑↑↑↑↑ 7/21 7/26 7/1 7/16 7/31 8/5 8/10 8/15 Q

The graph of the cosine function has been vertically compressed by a factor of 3, reflected in the y-axis, has a period of 720°, has been shifted left 60°, and has been shifted up 5. Write the equation of this function.