Trigonometry

1 - cos x as x approaches 0.

what is the cos of 0? It is 1.

So as x approaches 0 cos x approaches 1.

1 - 1 = 0

So as it gets very small the solutions gets smaller.

The function sec(x) is the secant function. It is related to the other functions by the expression 1/cos(x). It is not the inverse cosine or arccosine, it is one over the cosine function. Ex. cos(pi/4)= sqrt(2)/2 therefore secant is sec(pi/4)= 1/sqrt(2)/2 or 2/sqrt(2).

slope intercept formula is given by y = mx+c where m is the slope and c is the x intercept

so ur equation comes to... y=(0.25)x + 24

Yes.

An equation that is not a function is called a relation. Functions are special types of relations where every input (or in other words each value in the domain) has exactly one output (or matches up with exactly one value in the range).

A relation would be where you plug in a number for x but instead of only getting one number out for y, you get more than one. Example:

y2=x

If you plug in 4 for x and solve for y by taking the square root, then y could equal either positive 2 or negative 2, since 22 is 4 and (-2)2 is also 4. In this case, x corresponds with two output values for y (2 and -2) which means that while this equation is a relation, it is not a function.

Domain here would refer to all numbers that make sense for x. In other words, what numbers can you plug in for x, and get an answer that is not imaginary or undefined. In the example above, I could not plug in negative numbers for x, because when I try to solve for y I would get an imaginary number. So we would say that the domain of that relation is x> or equal to 0.

The Range for a relation is all of the possible output values. So for all the values of x that you can plug in, what are all the possible values of y I could get out? If you look at it, since I'm only plugging in 0 for x or any other number larger than 0, that would imply that y can only be 0 or bigger as well. So the range here would be y > or equal to 0.

I hope that helps!

tan(30 deg) = 0.5774, approx.

1.1519+k*pi radians or 66+180*k degrees for all integers k.

The sine of an angle is obtained from a right angle triangle. The other two angles are acute, or less than 90 degrees. The sin of the angle is the side opposite the angle divided by the hypotenuse.

in trigo..180 degees = ∏ radians.. so 510 = 180*2+ 150 = 2∏ + 5∏/6 =17∏/6

cos(x)=sin(x-tau/4)

tan(x)=sin(x)/cos(x)

sin(x)=tan(x)*cos(x)

cos(x)=tan(x-tau/4)*cos(x-tau/4)

you can see that we have some circular reasoning going on, so the best we can do is express it as a combination of sines and cotangents:

cos(x)=1/cot(x-tau/4)*sin(x-tau/2)

tau=2*pi

The answer depends on what else you know about the shape.

The theorem is used for right triangles. It means the two smaller sides squared and added together equal the hypotenuse squared.

The three ways to use it will let you find the third side if you were given two other sides.

a2 + b2 = c2

b2 = c2 - a2

a2 = c2 - b2

If you mean practical ways to use it, then there are some examples:

1. Suppose you want to know how long of a ladder you need. The ladder would be the hypotenuse. The distance from the ladder to the wall at the floor is one of the shorter legs of the triangle, and the height of the wall is the other leg. So if you know how tall the wall is and how far you want the base of the ladder from the wall, then you can use the formula to calculate how long you need the ladder. Then you'd round up to the nearest available size.

2. Perhaps you need the height of a tower. You can measure from the base to a convenient viewing spot. Using surveying equipment, you can get the angle to the tip of the tower and then use trigonometry (tangent function if I remember right) to calculate the length of the hypotenuse. Then you'd subtract the distance of the base squared from the calculated length squared to get the height of the tower or other object.

3. You can calculate the distance you saved by cutting through a lot as opposed to going around the corner. You've always heard that a straight line is the shortest distance, and you can use the formula to find out how much. For instance, lets say the lot is 3 feet by 2 feet. That is five feet if you take the corner. If you cut through, you are taking the hypotenuse. So lets calculate that distance. A2 is 9 (3 x 3). B2 is 4 (2 x 2). That means C2 is 13. So C must be 3.61 (if you round up). It is nearly 1.39 feet shorter cutting across than going around.

There are several ways to look at it....

The peak amplitude of the functions y = sin(x) and y = cos(x) is 1.

The peak-to-peak amplitude of the functions is 2.

The RMS (root mean square) amplitude of the functions is the reciprocal of the square root of two (2-½ ≈ 0.707).

360o - 215o

= 145o

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Twenty divided by the cosine of 32 gives you 23.584 ft

(sqrt 2) / 2

They are mathematical functions.

Most people are introduced to them as trigonometric functions. In the context of a right angled triangle, with one of its angles being theta,

Cos(theta) = The ratio of the lengths of the adjacent side and the hypotenuse.

Sin(theta) = The ratio of the lengths of the opposite side and the hypotenuse.

More advanced mathematicians will know them simply as the following infinite series:

Cos(theta) = 1 - x2/2! + x4/4! - x6/6! + ...

and

Sin(theta) = x/1! - x3/3! + x5/5! - x7/7! + ...

n! = 1*2*3* ... *n

That depends on the value of the angle, theta. csc is short for "cosecans", and is the reciprocal of the sine. That is, csc theta = 1 / sin theta.

negative one half

You must think of the unit circle.

negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example:

cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4

Remember that tan = sin/cos.

So your expression is sin/cos times cos.

That's sin(theta).

sin(1,305) = sin(225) = -0.70711 (rounded) = 1/2 of the negative square root of 2.

There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets,electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology),seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering,mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets,electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology),seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering,mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

A polygon is a plane figure which comprises one area bounded by three or more straight line segments. A general plane figure can have curved boundaries or sides that cross each other.