Trigonometry Answers

Is the graph of y = sin(x
5
) increasing or decreasing when
x = 12? (enter increasing, decreasing, or neither).
Is it concave up or concave down? (enter up, down,
or neither).

What is “harmonic motion”? How can harmonic motion be described mathematically? Be sure to link correct mathematical terms to correct physics terms – for example, how are the amplitude, period length, and other mathematical properties of harmonic motion waves related to how an object is moving? What is Hooke’s Law, and what does it have to do with harmonic motion? What is a spring constant, and what does it have to do with harmonic motion? Provide a couple of real-life examples of objects that move, roughly, according to simple harmonic motion

What is “sound”? How can sound waves be described mathematically? Be sure to link correct mathematical terms to correct physics terms – for example, how are the amplitude, period length, and other mathematical properties of sound waves related to pitch, tone, volume, and other physical properties of the sound wave? What is a “beat” pattern, and when does it happen? Why does a beat happen?

Find the absolute maximum and minimum values of f(x)=x−2x+4, if any, over the interval (−4,1].

absolute maximum is
and it occurs at x =

absolute minimum is
and it occurs at x

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 13 cm. (Note the answer is a positive number).

A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 8 volts is put across a resistance that is increasing at a rate of 0.3 ohms per second when the resistance is 3 ohms, at what rate is the current changing? (Give units.)

A rectangle has one side of 9 cm. How fast is the area of the rectangle changing at the instant when the other side is 19 cm and increasing at 5 cm per minute? (Give units.)

Find the equation of the tangent line to the curve y=2sec(x)−4cos(x) at the point (π/3,2). Write your answer in the form y=mx+b where m is the slope and b is the y-intercept.

(1 point) If k≥1, the graphs of y=sinx and y=ke−x intersect for x≥0. Find the smallest value of k for which the graphs are tangent.

Longitude and latitude are measured in degrees, minutes, and seconds. This is quite similar to the measurement of time. Why is this so?