Trigonometry

amplitude =7. to find the period, set 2x equal to 2∏. then x=∏=period

The two square roots of i are (k, k) and (-k, -k) where k = sqrt(2)/2 = 1/sqrt(2).

Used often in physics in finding vectors, such as current pull on a moving object. A ship going NE at so many knots while a cross current is going SE at so many knots. What would be the angle of travel sort of problem. Used all the time.

The absolute value of the sine function cannot exceed 1 and so sin(a) = 312 is not possible.

It is frequently used in mapping surveys.

For example, if you want to find the distance to a mountain peak, you would find the direction to that peak from two locations and measure the distance between those two locations. Triangulation based on trigonometry for the ASA triangle would enable you to work out the distance to the mountain peak without having to go there.

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

I will solve all your math problems. Check my profile for more info.

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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By using the sine ratio, you know two sides of the right triangle (the opposite and hypotenuse) and so can work out the third side (adjacent) using Pythagoras (opposite2 + adjacent2 = hypotenuse2).

You can then use the trigonometric ratios to calculate cos θ, sec θ, cot θ, and the hypotenuse you already have.

Sin θ = opposite/hypotenuse = 2/x

⇒ opposite = 2, hypotenuse = x, and adjacent = √(x2 - 4)

Thus:

cos θ = adjacent/hypotenuse = √(x2 - 4)/x

sec θ = 1/cos θ = hypotenuse/adjacent = x/√(x2 - 4)

cot θ = 1/tan θ = adjacent/opposite = √(x2 - 4)/2

Hypotenuse = x.

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.

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!

Positive or negative 4i

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

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. :)

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.

21metres

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.

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

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.

Suppose the distance is x.Then tan(25) = x/149 m so that x = 149*tan(25) metres = 69 metres, approx.

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.