A long branch of a pine tree is moving up and down in the wind such that the height (above ground) of a pine cone at the end fluctuates between 6 m and 7 m. The period of this movement of the pine cone is 3 seconds. Suppose that time t (in seconds) is defined so that at t = 1 second the pine cone is at height 7 m. Assume that the height (in metres) of the pine cone can be represented by a trigonometric function f(t). (a)  What is the mid-level of the pine cone’s height? (b)  What is the amplitude of f(t)? (c)  Find the smallest value of t > 0 for which f(t) = 6.     (d) Find a formula for f(t), showing all your reasonin

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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.

2) A 50 foot diameter Ferris wheel is constantly turning at four revolutions per hour. The bottom of the Ferris wheel is 10 feet of the ground. Graph the height of the Farris wheel as a function of time, f(t), if the starting time is when the Farris wheel is at the highest point. Be sure to state the angular frequency, period, amplitude, and midline of the function. Angular Frequency: Period: Amplitude: Midline: 2a)Write a possible formula for the cosine function f(t) represented by the information and graph from question 5.

Write the equation of a sine function that has a maximum at (70°, 3) and a minimum at (160°, -5)

In the theory of biorhythms, sine functions are used to measure a person's potential. Shown below is a person's chart beginning February 17. 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 April for the person to meet an online friend for the first time? Physical Intellectual Emotional Plus Zero Minus -1 217 2/27 3/19 3/14 3/24 4/8 4/18 4/13 3/9 2/22 3/29 4/3 3/4 4/23 The best day would be April (Type a whole number.)

You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour

The position of a honeybee flying up and down a straight flowerbed is given by (the euqation ) where t is measured in seconds and s is measured in meters. Positive values of s indicate that the bee is to the right of the center of the flowerbed, while negative values of s indicate that it is to the left of the center. (a) Use the graph to guess the time(s) at which the velocity of the bee is 0, and then use calculus to confirm the answer (b) How fast and in what direction is the bee flying at t = 3.5 seconds?  (c) Find the velocity of the bee at all times when its acceleration is zero.

Draw an arc of length [(11π)/(6)] on the unit circle and write the terminal point where the arc stops. Use the terminal point to give the exact values of the six trig functions.   Do by algebra/pre-calc techniques please! No Calc please. Thank you!

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