Trigonometry

An inrease in the retirement age would effectively increase a country's labor supply, shifting the production possibilities curve right.

because one side is concave and the other is convex

Geometry is the study of all shapes. This includes octagons. Trigonometry developed much later than geometry for applying the study of triangles to practical application.

You cannot.

Geometry (Greek γεωμετρία; geo = gaia or earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century B.C., geometry was put into an axiomatic form by Euclid, whose treatment - Euclidean geometry - set a standard for many centuries to follow. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere, served as an important source of geometric problems during the next one and a half millennia. However, the real problem with geometry is that these shapes we speak about are not, in reality "geo" or of earth, but rather in our minds as mental gymnastics. That is why calculus was developed in an attempt to measure the curvatures that elude geometric forms' more linear factors. Essentially, the circle is considered classically as a geometric form and perhaps should be. But the problem remains that albeit a circle would be more relevant to physical life as of it curvature, the problem remains of its measured exactitude. Since we have pi radius squared as the area of circle, we find that "pi" is a fraction and therefore, not exact. Classical math tries to dodge this question regarding the inexactness of a circle claiming equations exist to measure it exactly, but even the Fibonacci sequence is a fraction at 1.625 (some argue 1.618, but do the math of the square root of 5 minus 1 divided by 2). Therefore, the exacting factor means nothing and we must move on from there. It is similar to Einstein's claim to fame because his deflection of light theory was .83 of second arch more than Newton's at .87 second. Who cares about these exiguous degrees when 2/3 of the world is starving? We spend 200 million dollars on the restoration of the Parthenon in the past thirty years equating an obvious misprioritization when our neighbors starve to death. How sad.

-- Determine the number of revolutions, vibrations, reciprocations,

or full oscillations in one second.

-- Multiply that number by (2 pi).

An angle less than 90 degrees is an "acute angle". An angle of exactly 90 degrees is a "right angle". An angle more than 90 and less than 180 degrees is an "obtuse angle". An angle of exactly 180 degrees is a "straight angle". An angle of more than 180 degrees is a "reflex angle".

The horizontal part of the crane (the top of the 'T') is assembled on the ground first then jacked up for the first section of the tower to be inserted. The assembly is continually jacked up allowing more and more sections to be slotted in until the required height is reached. Some towerblocks are built in a similar way with the roof first being assembled at ground level then jacked up for floors to be built below. These are known in the UK as "jack blocks" but I'm not sure whether this is an official term or an international one for that matter. Alasdair Bailey

1. frequency
2. amplitude
3. phase angle

Yes: it is already in terms of y so nothing needs to be done.

It's not. A fixed point is where the function crosses the axis and so the (first) fixed point of cosine is pi/2 in radians, 90 in degrees and 100 in grad. I say first fixed point because it has another fixed point at 3pi/4 in rad, 270 in deg and 300 in grad.

To show it by iteration with rad, use the N-R equation xn+1=xn- f(xn)/f'(xn) which gives us xn+1=xn+cos(xn)/sin(xn) if we start with an initial point x0=pi/4=0.785398163 then the iterations give us:

x1=1.785398163

x2=1.567440065

x3=1.570796339

x4=1.570796327=pi/2 to 10 s.f.

There's some confusion here about the phrase "fixed point". 0.7390851332 is a fixed point in the sense that cos(0.7390851332)=0.7390851332 . This is not to be confused with stationary point.

Students are taught trigonometry so they meet the needs in architecture, astronomy and in other fields because trigonometry is the branch of Maths and maths is being used everywhere.

The word would be "ten thousand" multiplied by itself.

Given a unit circle (radius = 1) and a counterclockwise angle (theta) between the positive x axis, with the x-y coordinate of the point on the circle that the angle intersects, the three basic trigonometric ratios are... 1. sine (theta) is y 2. cosine (theta) is x 3. tangent (theta) is x / y

You have to take that up with your professor and/or your student advisor. WikiAnswers is not the place to ask those kind of institution specific questions.

Divide -900 by 360, and the remainder will be the angle you need to find the sine of: -900 / 360 = -2.5 --> -900 = 360*(-2 - 0.5), so sine(-180°) = sine(-900°).

sine(-180°) = 0

While there are formulae that can be used, they are certainly not simple and there is pretty much no way around this fact.

One such way to calculate this volume is to first work out the volume of the sphere, then the volume of the section you are removing the "top" of, and subtracting these volumes to determine the volumes of the large and small sections. This assumes that the slice is one plane (i.e. you took one slash with a straight edge in a perfectly straight line).

Assuming the sphere is centered at the origin (x=0, y=0, z=0) with radius R, and that the slicing plane is perpendicular to the x axis, slicing somewhere between x=-R and x=+R, then the volume of the "truncated" sphere is PI R2x + 2/3 PI R3 - 1/3 PI x3. This answer is the "simple" answer, for the case of only one plane, and it applies to all cases due to symmetry.

Deriviation, with most intermediate steps removed...

Start with a circle centered at the origin, with radius R. This is the projection of the sphere into two-space, or the slice of the sphere by the plane z=0. Draw a right triangle from the origin to any point (x,y) with distance R, i.e. on the circle.

Note that R2 = x2 + y2. Going back to the three-dimensional image of the sphere, note that y is the radius of a circle perpendicular to the x axis, and that it represents the slicing plane.

The area of that circle is PI (R2 - x2).

The volume of the truncated portion of the sphere to the left of x, i.e. between -R and x is the definite integral from -R to x of PI (R2 - x2) dx. This is a first year calculus problem involving stacking circles of known area with thickness dx, as dx approaches zero, to determine the volume.

Calculus majors will note that this is a trivial problem, and no one should need any further steps. The only thing to watch is the sign of x3 when x is negative.

Trigonometry majors, with all due respect, will probably not understand any of the further steps, so they are not presented. Besides; the original question was categorized as trigonometry, and it requested a "simple" answer, which has been provided above.

Depends on what is given. SOHCAHTOA where O=opposite side, H=hypotenuse, A=opposite sides of a triangle in relation to the angle you are seeking.C=cosine, S=sine, T=tangent. So it depends on what is given and what is sought to be any more specific!

Yes, sine, cosine, tangent definitions are based on right triangles

Greek. Essentially, "white blood".

Sine can be found in degrees by taking the length of the opposite side and hypoteneuse. Then divide the opposite side by the hypoteneuse. Any calculator can be used to find this.

for example, if the hypoteneuse side was 7, and the opposite side was 3, and you labeled the angle "A", then it would be "sineA= 3/7" ...... then A=sin^-1 (3/7) and you put that in your calculator and the answer you get is the angle in degrees (if the calculator is in degrees mode, and if the angle is an acute angle).

It has 8 factors if you include complex factors. Otherwise there are only 4.

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inverse of sin(15/20)