Trigonometry

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On a Cartesian plane (or one using polar coordinates), the vertex of the angle must be at the origin and one of the rays must lie along the positive x-axis (point towards the East).

The Arabs invented the modern math of trigonometry. They used Ancient Greek proofs (such as those made by Pythagoras and Demosthenes) to discover that the relationships between the lengths of sides of a right angle triangle were consistent when the angles were consistent. They proved methods to derive the proper value relationships, resulting in the trigonometry tables that have now been plugged into in every scientific calculator.

According to Star Trek, Earth is located in the Alpha Quadrant (50000;74000). This is based off the Cartesian planar coordinate system with the upper left corner (0;0) and the lower right corner (100000;100000). The zero-point of the system is located in the center of the Galaxy, and the 4 quadrants correspond to the 4 Galactic quadrants (Alpha=III, Beta=IV, Gamma=II, Delta=I). Consequently, the system has the advantage that the Galactic quadrant can be easily determined by the sign of the x and y coordinates: position in Alpha Quadrant - x negative, y negative; position in Beta Quadrant - x positive, y negative; position in Gamma Quadrant - x negative, y positive and position in Delta Quadrant - x positive, y positive.

Companies write it off if they can not claim payment for the estate and the family does not pay it. The family is only responsible if their name is on the bills with the deceased. In most situations when monies can not recovered due to death, they the company writes odd the debt as bad debt. The estate of the deceased is responsible for contacting all possible debtors and informing them of the death. They are also responsible for a full inventory of the assets of the estate. If the assets are greater then the debts, all debts will get paid off and the rest distributed to the heirs.

No because Pythagoras' theorem states that for any right angle triangle its hypotenuse when squared is equal to the sum of its squared sides.

what is the application of trigonometry in your life and future carrier

Are there infinitely many multiples of 11 with an odd digit sum?

Yes.

One proof [I'm not sure that this is the simplest proof for this, but it is a proof]:

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Note that 209 is divisible by 11 and has an odd digit sum (11). Now consider the number 11000*10i+209. Because 11000 is divisible by 11 and 209 is divisible by 11,

11000*10i+209 is divisible by 11 for all whole number values of i (of which there are infinitely many).

Further, the digit sum for 11000*10i+209 is odd for all whole number values of i because the hundreds, tens and ones places will always be 2, 0, and 9 respectively, and the other digits will be either all zeros (for i=0) or two ones followed by zeros, down to and including the thousands places. Thus, the digit sum of 11000*10i+209 is 11 for i=0 and 13 for all other whole numbers i.

Thus, we have have the following set of numbers (of which there are infinitely many) which are multiples of 11 and which have an odd digit sum:

209
11209
110209
1100209
11000209
110000209
.
.
.
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[Note there are other multiples of 11 that have an odd digit sum (e.g., 319, 11319, 110319, ...).]
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Late addition:

Here is the simplest proof:
Prove that x+2=3 implies that x=1.

proof:
FIRST, assume the hypothesis, that x+2=3. What we try to do is reach the conclusion (x=1) using any means possible. I have some algebra skills, so I'll subtract 2 from both sides, which leads me to x = 1.
QED.

You would have to find the adjacent and the hypotenuse. For example, if the adjacent was 80 degrees and the hypotenuse 29 you would do this: cos(29)/29 which wiuld give you 0.03. When finding the cosine its adjacent over hypotenuse. For sin its opposite over hhypotenuse and for tan its opposite over adjacent.

cos(125) = cos(180 - 55) = cos(180)*cos(55) + sin(180)*sin(55)

= -cos(55) since cos(180) = -1, and sin(180) = 0

So A = 55 degrees.

Yes of course it can, all of these mathematics evolved from Vedas.

tangent(54) is about 0.673800101

You need to use special triangles in order to do this. Special triangles are right triangles with specific angles for which we can determine the ratio of the side lengths. This ratio can be represented as a fraction, which could be used to answer a question like this.

For the examples you posted, there is the 30-90-60 degree special right triangle. The ratio of the sides is 1, 2, and square root of 3. The 2 is the side opposite the 90 degrees and is the hypotenuse of the triangle. The 1 is the opposite side of the 30 degrees and the square root of 3 is opposite of the 60 degrees.

To find the sine of 60 degrees, imagine 60 degrees represented on a graph as a triangle. The side opposite of the 60 would be the square root of 3, while the hypotenuse is 2. Sine is opposite over hypotenuse, so the answer to this would be the square root of 3 divided by 2.

For the cosine of 150 degrees, imagine 150 degrees as a line on a graph in the second quadrant. Now form the special triangle with the line and the x axis. You'll have a special triangle with 30 degrees in the corner by the origin, as 180-150=30. You can then find the cosine of this 30 degrees using the ratio of the sides mentioned above.

Always make sure to form the triangle with the x axis. Another common special triangle is the 45-90-45 degrees one. The hypotenuse (opposite the 90 degrees) is square root of 2 and both the other sides are 1.

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well, nothing is for sure but it is said that Hipparchus, a Greek geographer. its kind of odd though. but they say that they have evidence of his systematic use of trigonometry. Also Menelaus and Ptolomy helped in the development of trigonometry.

The basic equation is of general form y = R(x) where (here) R is the Sine, Cosine or Tangent of x, and consequently the Sine and Cosine curves plot oppositely from +1 via 0 to -1 (minus 1) over 180º. The y-values of the Tangent curve goes cyclically from 0 to infinity as x goes from 0º to 90º: it looks odd at first, and you might even think you've gone wrong!

Plot in the usual way: left-hand column or top row for suitable increments of x = [angle in degrees], neighbouring columns or rows below for the corresponding ratio values. To get the best out of it, plot 0º to 360º, to give a whole Sine Wave cycle - it and the Circle to which it can be related geometrically, being perhaps the 2 most important curves in Nature!

Because any angle increased by k*2pi radians (= k*360 degrees) where k is an integer, is, effectively, the same angle. This implies that f(x + 2kpi) = f(x) for any angle x and any trig function f. This gives f a maximum period of 2pi radians.

There is no proof. 1 mechanical horse power is simply defined as 745.7 watts. Period.

It has no roots because the discriminant of the given quadratic equation is less than zero.

There is no minimum value for the cosecant function.

Yes

Exact solutions of trigonometric equations those in which you leave values like pi or square roots in the answer rather than their decimal approximations.

So, for example, the exact value of sin(60 deg) is sqrt(3)/2, not 0.8660

Bernoulli's Principal is as the speed of a fluid (liquid or gad) increases the pressure of the fluid decreases. The shape of an airplane wing causes the air to move faster over the top of the wing, thus lifting the wing up.

Origin