Pre Cal probs dealing with sinusoids
[IMG]file:///Users/erin/Library/Caches/TemporaryItems/moz-screenshot.jpg[/IMG]I need help with these! If I have made headway on the problems, I have posted what I have below each problem. I need to know if I am right or headed in the right direction! The ones that are blank I have no clue.
1. A signal buoy bobs up and down with the height h of its transmitter (in feet) above sea level modeled by h = asin bt + 5. During a squall its height varies from 1 to 11 feet and there are 5.6 sec from one 9th height to the next. What are the values of the constrains a and b? Write the equation of the sinusoid of the buoy.
H=asin bt + 5
A =Amplitude = |a| = (11-1)/2 = 10/2 = 5
B = Period = 2π/b = 2π/ 5.6 = (2/1)(1/5.6) = 2/5.6 = .357 π
New Equation : h = 5sin (.357 π (t)) + 5
2. Tsunami Wave. An earthquake starts a tsunami in the ocean. It produced waves that traveled more than 540 f/sec and reached a height of 60 ft. If the period of the waves was 30 min, estimate the length between crests.
You are supposed to know that the distance d traveled at a speed v in the time t can be calculated by:
D=v x t
Transcribe 30 minutes into seconds: 1800 seconds
The distance from peak to peak is:
D=540 x (1800s)(ft/s)=972,000 ft=184.1 miles
3. A Ferris wheel 50ft in diameter makes one revolution every 40 sec. If the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50tf above the ground. Show a diagram and all algebraic/trigonometric work.
50-30/25 = sin ((2pi/40) *t - (pi/2))
.08 = sin ((2pi/40) *t - (pi/2))
how do i solve for t??
4. Draw a graph of y = csc x, in relation to a basic trigonometric function showing 2 periods, show all points of interest, and write a description of the csc wave in paragraph form.
5. Use segment names to show the compound-angle identity of your choosing, use either sin(u + v) or cos(u + v). (note cos or sin (0 Ė 0) is not acceptable). Include a diagram