Trigonometry

43.3

Various trigonometric functions, such as sine or cosine, show the relationship between the lengths of sides of a triangle and the angles between those sides. So trigonometry is used to calculate angles, lengths and distances using right triangles. Right triangles are those that have one angle of exactly 90 degrees.

Example: You want to find the height of a tree. Measure off a fixed distance from the tree and measure the angle between the ground and the line-of-sight to the top of the tree. The height of the tree = the distance to the tree times the tangent of the angle between the tree and the ground, ie tan(x).

The answer is rather complicated but I will do my best. Let's consider logs in base 2 as those are the easiest. We can make a table quite easily:

log2_1 = 0

log2_2 = 1

log2_4 = 2

log2_8 = 3, etc.

Notice that in order to get a whole number answer we had go by powers of 2. So we know the logarithms for 2, 4, 8 etc. But what if we want to find the logarithm of say 3? Now I don't quite remember where I saw this but to find a logarithm between two others we take:

logB_square root[X * Y] and [C + D] / 2 with the logs being logB_X = C & logB_Y = D with the log being between them. For example take:

log2_2 = 1 and log2_8 = 3 using the formula we get log2_sqrt[2 * 8] = [1 + 3] / 2 =

log2_4 = 2 which you can clearly see is between the two logs. Now to find log2 = 3 we take:

log2_2 = 1

log2_4 = 2

sqrt of 2 * 4 = 2.828 approximately and [1 + 2] / 2 = 0.5 so we get:

log2_2.828 = 0.5; to get closer that 3 is between log2_2.828 and log2_4 so using the formula on them we have: sqrt [2.828 * 4] and [0.5 + 2] = 1.25

log2_3.63 = 1.25; then continuing a few times:

log2_3.20 = 0.875; used log2_3.63 and log2_2.828

log2_3.00 = 0.6875; used log2_3.20 and log2_2.828

We can keep going getting closer and closer to 3. We got 3.00 because I was rounding the answers on the calculator. We can actually go on forever always getting closer. We stop when we notice we start getting the same answer. Notice that each time we used the formula we kept the log we wanted in between the 2 logs we used. This is IMPORTANT! If the log you want isn't in between the logs you use for the formula you will not get the right answer. Now this nowhere near precise but I hope you get the idea. To get more accuracy you should keep more decimal places. Like if you want 5 decimal places keep 6 and then when you're done round your answer. Also note that there is formula to change the base. It is:

[logB_C] / [logB_D] = logD_C

So once you make a table of logarithms in one base you can use the formula to conver them to any base you wish. I can always help clarify if anyone has trouble getting this.

None.

A trapezium is a rectangle with its top line shorter then the bottom one.

Jonathan Sisson invented the theodolite, which measures both horizontal and vertical angles, in 1720, according to the Alberta Land Surveyor's Association. This instrument resembles a mounted telescope, and a user can adjust the height of the platform so his eyes are level with the ocular lens.

Find the area of a triangular section, 1/2bh, and then multiply by the length of the prism.

Just like most any other set of functions, trigonometric functions are subject to differentiation. Trig functions are cool (at least sin and cos are) because as you differentiate, they cycle through until you get back where you started.

Just Look Around Or If Worse comes to worse buy a trig text book

thanks you for your help

find the volume & total surface of a square pyramid, the side of the base being 4meters & height 5meters

360 / 4 = 90 It is 90 degrees

You need to specify what quantity you're trying to find.

arya bhat is very good man who invented the no. o. agar hamare pas zero na hota to hum kahan hote.

That's a hexagon !

v = lcos^-1 (1-(y/r))r^2+l sqrt[(2r-y)y](y-r)=pi (ry^2-(y^3/3))

where v=volume, y=height of liquid in tank, r=radius of tank, l=Length of tank

Or you can just use this:

http://grapevine.abe.msstate.edu/~fto/tools/vol/parthcylinder.html

The answer depends on formula for WHAT! Its surface area, number of edges, mass, volume. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.

A reflex angle

When you study the theory of geometry, it is pure mathematics.

However, when you start using the geometry you have learned in other, more practical areas, then it becomes applied.

Linear equations come in the form y=mx+b or y=mx-b, where x and y are the variables x and y and b is a constant (like 3). All other equations are non-linear.

Linear equations has a power of 1!

as long as the X has a power of 1, it is a linear equation.

This is somewhat difficult to explain without images, but here goes:

You can use the information given in the problem to draw a right triangle on your coordinate axes. The hypotenuse of this right triangle should extend from the origin to point P and make a 50 degree angle with the x-axis. We'll call this hypotenuse r, which in this case is 1 (because we're dealing with the unit circle). If you extend a line down from point P perpendicular to the x-axis, the segment formed, which we will call y, will be the side of the right triangle opposite the 50 degree angle. The remaining side, x, lies along the x-axis between the origin and the point where side y intercepts the x axis.

Recognize that side x and side y represent, respectively, the x and y coordinates of P. These values can be found using trigonometric relationships.

Recall that sin(a) = opposite/hypotenuse. In this case, a = 50, the opposite side is y, and the hypotenuse is r=1, so we can rewrite this equation as

sin(50) = y/r = y

Which means that y is simply sin(50).

Similarly, cos(a) = adjacent/hypotenuse, so cos(50) = x/r = x. x = cos(50).

P is therefore located at (cos[50], sin[50])

A trapezium is a 4 sided quadrilateral with a pair of opposite parallel sides that have different lengths

im 101% sure that the answer is a cuboid im a mathmetishion and i know my stuff real well. i hope this helps you with any homework given to you and in the meantime farewell.

It allowed points in space to be described algebraically. This allowed lines and curves to be described using algebra. Bringing together algebra and geometry meant that tools that mathematicians had developed for solving algebraic problems could be applied to problems in geometry and tools from geometry could be applied to algebra.