Tutors Answer Your Questions about Trigonometry-basics (FREE)
Question 481747: two objects are directly in line with a cliff which stands 282ft. above the water. there angles of depression from the top of the cliff are 42 degree 25 minutes and 37 degress 15 minutes. how far apart are the objects and what are their horizontal distance from the cliff?
Click here to see answer by mananth(12270)   |
Question 482014: tan 5pi/3 and i need to determine the exact value of the expression without a calculator. I know how to work with the circle but i dont understand what to do if its not in one of the main angles. How am i supposed to find the answer?
tan 5pi/3 is tan300 but its not a main angle what do I do?
Click here to see answer by richard1234(5390)  |
Question 482355: Please help: Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies. Set A is the set of all exercise classes offered at Gold’s Gym. Set B is the set of aerobic exercise classes offered at Gold’s Gym
Click here to see answer by Theo(3458)  |
Question 482685: Can you give an example of each of the following for real life use
ratio
proportion
direct variation
inverse variation
joint variation
rational equation
trigonometric function
right triangle
law of sines
law of cosines
vector
system of linear equations
determinant
quadratic equation
radian
factoring
completing the square
quadratic formula
phasor
complex number
exponet equation
logarithmic equation
decimal
binary
octal
hexadecimal
rectangular coordinate
polar coordinate
plane geometry
Click here to see answer by stanbon(57243) |
Question 482787: Trigonometry problem
hard to try and explain to you without the picture but I'll do my best
There's a right triangle ABC - where C is 90 degree the distance between C and B is 300 and the distance between and A and C is 100. There's half a cirle inside the triangle - what is the diameter of the circle (the other half of the circle is outside the triangle). If you wish to have a picture of this, let me know I can send it. thanks Louise
Click here to see answer by Alan3354(30983)  |
Question 486485: I have a line-segment on the Cartesian Plane. I know the endpoints by their distance from the origin and the angle from the x-axis.
To make it all simple, assume one point is on the x-axis.
I'll call the difference between these two angles the "angular-spread", for lack of a better education.
I need to know how to calculate a point on the line-segment given an angle that lies between these two points.
I've been trying to deduce the answer to this problem by graphing it in real time and analyzing the result. I've come up with some equations that sort-of work, but none work for every line, and I must guess at the factors involved for each line and fine tune it until I get an acceptable result. Not a workable solution. I was hoping at least I could begin to see the pattern and then be able to automatically calculate the factor. For five months my brain has been frustrated with this problem.
A simplified version of this problem is how to calculate the radial distance from the origin to the edge of a regular polygon inscribed within a circle centered at the origin, given an angle. The line segments do not “slope” in this problem. Assume one point of the polygon lies on the x-axis. (and I'll just call it a polygon henceforth, but I mean regular polygon)
Every way I address this issue, the line comes out curved.
At first I attempted to use the properties of tan and arctan to address this problem. This also allowed me to control the shape of the line to some extent without leading to illogical answers - I could plug in any positive number.
I then looked at it in a different way, and attempted to use the half-chord formula (  where a is the angular spread of the chord) to calculate the "in-radius" (I learned that term from your website: thanks!) and hence the difference between the radius and in-radius. Then by converting the angle of the point in question on the line to a ratio (angle = angle / angular-spread) I could try to calculate the difference via a sin curve. Once the distance from the origin is found, the point can be calculated from the known angle and calculated distance. Anyway, it's really the distance from the origin I ultimately want to know.
Here's that formula:
d? = the distance from the origin to the point in question.
a = the known (given) angle of the point in question.
s = the known "angular-spread".
r = the known radius of the circle that contains the polygon; i.e. the distance from the origin to any and every corner of the polygon.
Things get more complicated when the line segment has ends that are not equidistant from the origin. The Angle that bisects the "angular-spread" no longer bisects the line segment, but perhaps that ultimately doesn't mater - it correctly factors for the "slope" (I'm using slope in a metaphorical way - I suppose it's a slope on the polar grid...).
Here are more formulas I've tried that attempt to define any line inscribed in a circle by a given angle, a given "factor" (any positive number, but must be fine tuned "by hand"), and known endpoints based on their angle and distance from the origin:
d? = the distance from the origin to the point in question.
a = the known (given) angle of the point in question.
s = the known "angular-spread".
f = the given factor
r1 = the distance from the origin to the first point
r2 = the distance from the origin to the second point
I'm working on an open source (free for all to use and or modify) software project for creating graphics using modern image formats (.png alpha transparency) in ways that are not supported by most other graphic design programs. I'm writing it in the PHP language, which is fairly simple to read by even a non-programmer to some extent. Mathematical formulas are understandable, I think.
Use Open Office draw to create a star, and fill that star with a "radial gradient" and you get a circular radial gradient that shows through a star-shaped mask. I want a star-shaped gradient! The same goes for any other shape.
I've got a working solution that not only does this, but allows you to create multi-colored gradients with multiple transparency gradients. It does circles, ellipses, stars (using the formulas above – note how these formulas allow me to “swell” the sides out, or pull them inwards, an effect I want), polygons (using the one formula above), and others not easily described here. It just doesn't do perfectly strait edges...yet
It can even take your basic shapes and place them repetitively in a ring on the polar grid. That makes some really cool effects. I could go on and on about how this software is great, but it is NOT a replacement for other desktop image creation software, and will never be sell-able in that respect. PHP is far too slow.
If you're curious, you can see the central color-highlighted code (easy to read when highlighted by color) here:
http://softmoon-webware.com/rainbow-maker/Rainbow.htm
You can get the entire software package here (but you will need a working server with PHP, at least until PHP becomes a stand-alone package that works with browsers - i.e. it's own server - that you can install on your system.)
http://softmoon-webware.com/rainbow-maker/rainbow-maker.7z
You can get an simple-to-install server package with Apache and PHP (and more) using XAMPP from the Friends of Apache:
http://www.apachefriends.org/en/xampp.html
Then you can use this as a desktop application using your browser.
A working example is also found at:
http://softmoon-webware.com/rainbow-maker/
But this will limit the size of the graphic created, because it's on a public server.
I took trig in college over 20 years ago – thanks to Wikipedia, I came up with this much so far. PLEASE help me finish it (if only so my brain will stop throbbing). All I need is a basic formula...
Aloha!
Click here to see answer by richard1234(5390) |
Question 486694: Two aircraft leave simultaneously from an airport, one flying due north and the other due east. The northbound aircraft averages a speed of 100 miles per hour fater than the eatbound aircraft. After 3 hours, the aircraft are 1500 miles apart. Find the average speed of each aircraft.
Click here to see answer by mananth(12270) |
Question 457336:
I have choose 16 coins to work with
SHAKE HEADS TAILS
1 8 8
2 7 9
3 11 5
4 9 7
5 6 10
6 12 4
7 1O 6
8 3 13
9 7 9
10 14 2
11 8 8
12 6 10
13 7 9
14 5 11
15 10 6
16 8 8
Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow the coins to be shaken around. Shake the bag well and empty the coins onto a table. Tally up how many heads and tails are showing. Do ten repetitions of this experiment, and record your findings every time.
State how many coins you have and present your data in a table or chart.
Consider just your first count of the tossed coins. What is the observed probability of tossing a head? Of tossing a tail? Show the formula you used and reduce the answer to lowest terms.
Did any of your ten repetitions come out to have exactly the same number of heads and tails? How many times did this happen?
How come the answers to the step above are not exactly ˝ and ˝?
What kind of probability are you using in this “bag of coins” experiment?
Compute the average number of heads from the ten trials (add up the number of heads and divide it by 10).
Change this to the average probability of tossing heads by putting the average number of heads in a fraction over the number of coins you used in your tosses.
Did anything surprising or unexpected happen in your results for this experiment?
Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.
What is the probability for each of the outcomes?
Which kind of probability are we using here?
How come we do not need to have three actual coins to compute the probabilities for these outcomes?
Click here to see answer by levell(1) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495
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