Trigonometry

You can rationalize the denominator by multiplying this fraction by a fractional form of one in radical form.

3/sqrt(2) * sqrt(2)/sqrt(2)

= 3sqrt(2)/2

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Yes, this is a perfectly legitimate thing to do in the trigonometric functions.

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Positive or negative 4i

Say you want a bridge 400 m long. It will consist of 400 1 meter upside down triangles. Wait...it's a triangle, therefore you need to know how much material the other sides are! Well, worry know more, there are trig functions on calculators!

Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!!

a = 4 (angle opposite = alpha)

b = 5 ( angle opposite = beta)

c = 8 ( angle opposite = gamma )

a^2 = b^2 + c^2 - 2bc cos(alpha)

4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha)

16 = 89 - 80 cos(alpha)

-73 = -80 cos(alpha)

0.9125 = cos(alpha)

arcos(0.9125) = alpha

alpha = 24.15 degrees

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b^2 = a^2 + c^2 - 2bc cos(beta)

5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta)

25 = 80 - 64 cos(beta)

-55 = -64 cos(beta)

0.859375 = cos(beta)

arcos(0.859375) = beta

beta = 30.75 degrees

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Now to find gamma, subtract from 180 degrees

180 - 24.15 - 30.75

= 125.1 degrees

alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees )

beta = 30.75 degrees

gamma = 125.1 degrees

now you see the smallest, the angle opposite the a side, which is 4

( be in degree mode!!)

In an oil spill in the ocean, the oil rises to the top because it is less dense than water, creating an oil slick on the surface of the ocean. A Styrofoam cup is less dense than a ceramic cup, so the Styrofoam cup will float in water and the ceramic cup will sink.

a straight line equation is y=mx+c

where x is the first value of an ordered pair and y is the second (x,y)

m is the slope of that line

and c is the y intercept , the point that the straight line cuts y-axis

Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).

Yes.

Yes !!

Mathematics is a subject that is vital for gaining a better perspective on events that occur in the natural world. A keen aptitude for math improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. Now it's true that triangles are one of the simplest geometrical figures, yet they have varied applications. The primary application of trigonometry is found in scientific studies where precise distances need to be measured.

The techniques in trigonometry are used for finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps). Now those are the scientific applications of the concepts in trigonometry, but most of the math we study would seem (on the surface) to have little real-life application. So is trigonometry really relevant in your day to day activities? You bet it is. Let's explore areas where this science finds use in our daily activities and how we can use this to resolve problems we might encounter. Although it is unlikely that one will ever need to directly apply a trigonometric function in solving a practical issue, the fundamental background of the science finds usage in an area which is passion for many - music! As you may be aware sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry.

Trigonometry is used to find the distance and angle of atoms that are bonding. Oh this is for chemistry by the way hope this was helpful. :)

They are both equally accurate.

However,

sin(x) = sin(180-x) where x is in degrees. This means that the sin law cannot distinguish between, say an angle of 30 degrees and 150 degrees.

On the other hand,

cos(x) = -cos(180-x) and so has a unique solution for 0<x<180 which is valid range for angles of a triangle.

A logarithm is quite the opposite of an exponential function.

Whereas an exponential is y=ax , a log is logay=x

For example, log39=2 because you raise 3 by the 2nd power to get 9. In other words, log39=2 because 32=9

Logarithms are present because they are a handy way to solve exponential equations, and because calculators use them to great advantage.

The answers are: -5*-3 = 15, -8*7 = -56 and -4*-12 = 48

21metres

The square root of x to the seventeenth power is x to the eighth and a half power. If x is negative, the answer is imaginary.

By statistical analysis.

It is very difficult to calculate these using mechanics. Calculations of the trajectory of a projectile assume that the mass of the projectile is such that air resistance has a negligible effect. This is not the case when the projectile is confetti - even if it is packed densely to start with.

Consider the Complex Plane, with Real numbers along the horizontal axis, and Pure Imaginary numbers on the vertical axis. Any Complex number (a + ib) can be plotted as a point (a,b) on this plane. The point can be represented as a vector from the 'origin' (0,0) to the point (a1,b1). If the second 'complex vector' (a2,b2) is added to the first, this can be shown as a translated vector with it's 'tail' starting at the arrowhead of the first vector, and then the arrowhead of the second vector will terminate at the sum of: a1 + ib1 + a2+ ib2 [coordinate point: (a1+a2,b1+b2)

The TI-83 does not have the cot button, however, if you type 1/tan( then this will work the same as the cot since cot=1/tan.

The other way to do this is to type (cos(x))/(sin(x)) where x is the angle you're looking for. This works because cot=cos/sin

0.75

x= 30 degrees

first, subtract 3 from 4 and you get 2sinx=1

then, divide both sides by 2 to get sinx=1/2

by using a 30, 60, 90 triangle you can see that 1 is the side opposite theta and

2 is the hypotenuse

therefore, your answer is 30

An example of a real life exponential function in electronics is the voltage across a capacitor or inductor when excited through a resistor.

Another example is the amplitude as a function of frequency of a signal passing through a filter, when past the -3db point.