Trigonometry Answers

Trigonometric integrals

3 example

3 application real life

A weight on the end of a spring oscillating in harmonic motion. The equation model for oscillation is d (t) = 6 sin ((pi/2)(t)) where d is the distance (in centimeter) from the equilibrium point in t sec.

a. What is the period of the motion? What is the frequency of the motion?

b. What is the placement from the equilibrium at t = 2.5? Is the weight moving toward the equilibrium at this time?

c. What is the displacement from equilibrium at t = 3.5? Is the weight moving toward the equilibrium point or away from the equilibrium at this time?

d. How far does the weight move between t = 1 and t = 1.5 sec?

e. What is the average velocity for this interval? 

f. Do you expect a greater or lesser velocity for t = 1.75 to t = 2? Explain why.

Recent studies seem to indicate the population of North America porcupine (Erethizon dorsatum) varies sinusoidally with the solar (sunspot) cycle due to its effects on Earth’s ecosystems. Suppose the population of these species in a certain locality is modeled by the function P(t) = 250 cos ((2pi/11)(t))+ 950, where P(t) represents the population of porcupines in year t. Estimate the number of years the number of population is less than 740 animals.

Cos(5x)cos(2x) + sin(5x)sin(2x)

Sketch the 3 trigonometric functions of sin θ, cos θ and tan θ over one complete cycle, where 00 ≤ θ ≤ 360

Complete the sketches on separate graphs for the three trigonometric functions.

Find the volume of a frustum of a regular square pyramid if the base edges are 7 cm and 19 cm, and one lateral edge is inclined at an angle of 60 degrees with the lower base.

If cos(x) = -(5/13) and π/2 ≤ x ≤ π, find the value of sin(x) and tan(x).

On a walking holiday you travel from the start, 𝑆, 5km on a bearing of 60° to point 𝑃. Then you change direction and walk for 5km on a bearing of 300° arriving at the finish 𝐹. What is your distance and bearing now from the start? Draw a diagram as part of your answer. 

A wheel that is drawn by a belt is making 1revolution per second (r/s). If the wheel is 18cm in diameter, what is the linear velocity of the belt in cm/s? 

A bicycle with 20 inch wheels is travelling down a road at 15mi/h. Find the angular velocity of the wheel in revolutions per minute.