Trigonometry Answers

14. A fly, buzzing about the room, calculates the angle of depression of the base of an 8-foot wall is 33.7° and the angle of elevation of the top of the wall is 12.5°. Find to the nearest foot the horizontal distance the fly is from the wall.

13. A blimp is flying parallel to a road and is 2460 feet directly above it. The angles of depression of two parked cars on the road are 34.9° and 26.5°. TO the nearest foot, how far apart are the parked cars? (Note: The blimp is above a line between the parked cars.

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.