Trigonometry

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.

You can choose either or but tangent which is sin/cos seems to be the most common way.

x + y = 13 . . . . . . . . . . (A)2*x + 3*y = 1 . . . . . . . (B)

(B) - 2*(A) : y = -25

Then, by (A) x - 25 = 13 so that x = 38.

There are only three kinds of triangle - equilateral, where all three sides are the same - isoceles, where only two sides are the same - and scalene, where no sides are the same.

The right triangle is a special case of the isoceles or scalene. Even if you consider the right triangle different, which is is not, that only make five kinds of triangle.

The sine of an angle of a right triangle - which is a triangle containing one 90o angle - is calculated as the length of the side opposite the angle divided by the length of the hypotenuse.

For very small values of x, sin(x) is approximately equal to x.

There are many ways to find the area. We restrict the answer to a regular pentagon with is one with equal sides and angles.

One method uses the apothem which is a line segment from the center to the midpoint of any of the sides. We use the length of the apothem. In this case, the area is 1/2 x apothem x perimeter.

This method works for any regular polygon.

Here is a slightly more complicated method and explanationl

We have n sides, all equal length a

We have n interior angles, all equal measure beta

Alpha is the central angle subtending one side

P is the Perimeter

K is the Area

Let R be the radius of circumscribed circle and

r be the radius of inscribed circle.

The for any regular polygon we have:

beta = Pi(n-2)/n radians = 180o(n-2)/n

alpha = 2 Pi/n radians = 360o/n

alpha + beta = Pi radians = 180o

P = na = 2nR sin(alpha/2)

K = na2 cot(alpha/2)/4

= nR2 sin(alpha)/2

= nr2 tan(alpha/2)

= na sqrt(4R2-a2)/4

R = a csc(alpha/2)/2

r = a cot(alpha/2)/2

a = 2r tan(alpha/2) = 2R sin(alpha/2)

For a regular pentagon

Number of sides n = 5

Internal angles beta = 3/5 radians = 108 degrees

Central angles alpha = 2/5 radians = 72 degrees

Perimeter P = 5a = 5R sqrt(10-2 sqrt[5])/2

Area K = 5a2 sqrt(1+2/sqrt[5])/4

= 5R2 sqrt(10+2 sqrt[5])/8

= 5r2 sqrt(5-2 sqrt[5])

= 5a sqrt(4R2-a2)/4

Circumradius R = a sqrt(2+2/sqrt[5])/2

Apothem r = a sqrt(1+2/sqrt[5])/2 = R(1+sqrt[5])/4

Side a = 2r sqrt(5-2 sqrt[5]) = R sqrt(10-2 sqrt[5])/2

Yes, Anuita her older sister and a brother

Isosceles, right, acute, obtuse, scalene, equilateral, (anyone else feel free to tag on)

equiangular

-14 + 3p = -9p - 21

add 14 and 9p to both sides, then 12p = -7

p = -7/12

To solve equations with absolute values in them, square the absolute value and then take the square root. This works because the square of a negative number is positive, and the square root of that square is the abosolute value of the original number.

Yes, the law of sines can be used in a right triangle. The law applies to any arbitrary triangle.

The slope is a negative number.

A sine wave is a simple vertical line in the frequency domain because the horizontal axis of the frequency domain is frequency, and there is only one frequency, i.e. no harmonics, in a pure sine wave.

False.

The angles can be formed by two skew lines intersecting a third line.

Farmer John stores grain in a large silo located at the edge of his farm. The cylinder-shaped silo has one flat, rectangular face that rests against the side of his barn. The height of the silo is 30 feet and the face resting against the barn is 10 feet wide. If the barn is approximately 5 feet from the center of the silo, determine the capacity of Farmer John's silo in cubic feet of grain.

Hint: Look for connections between this problem and the problem you solved in Part 1 of this week's Discussion (a square inscribed in a circle).

Is this correct?

The volume of any prism is the area of the face multiplied by the height. The height is given, so all you need to find is the area of the base. Start off by drawing a circle. One side has a chord of length 10 feet cut across it. Its given that the chord is 5 feet from the center of the circle. Therefore, you draw a line from the center bisecting the chord, as well as a line from the center to each end of the chord (the radius), and you have two equal isosceles triangles with two sides of length 5. Pythagorean's relation tells us that the third side has a length of 5*sqroot(2) ft. Now that you have the radius, you can find the area of the circle. However, its not a true circle you're concerned with. You want to exclude the area on the outside of the chord. Using trig, you can find that the total angle subtended by the chord is 90°. Therefore, the area that you're concerned with is the circular area for the outside 270° plus the area of the triangles. 270° is (3/4) of the circle, so its area is (3/4) the area of the entire circle. A = (3/4)*π*r² = (3/4)*π*(5*sqroot(2)ft)² = 118ft². The area of each of the smaller triangles is given by (1/2)*b*h. Since there's two triangles, the total area of the two is 2*(1/2)*b*h = b*h = 5ft*5ft = 25ft². The total area of the base is 118ft² + 25ft² = 143ft². Multiplied by the height will give the total volume of the prism, 143ft²*30ft = 4290ft³.

If you know the length of the sides of a triangle you can find all the angles of the triangle using the Law of cosines such as:

Step 1.

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

cos B = (a^2 + c^2 - b^2)/(2ac)

cos C = (a^2 + b^2 - c^2)/(2ab)

Step 2.

Find the arc cosine A, arc cosine B, and arc cosine C in order to find the angles A, B, and C.

Zero.

The simplest geometric concept is an item that has no dimensions = a point. The next simplest is an item that has only one dimension = a straight line. The next simplest is an item that covers area but only needs one number to completely describe it . . . a circle.

moivre's formula

tan-1(0.4877) = 25.99849161 or about 26 degrees

Take corresponding points on two steps. The further apart these two points - the more steps between them - the more accurate the result will be.

Measure the horizontal distance between the two points (x) and the difference in height (y). If theta represents the angle of inclination of the staircase, then tan(theta) = y/x is the measure of the slope or steepness of the staircase.

To calculate the angle that the staircase makes with the floor, theta = arctan(y/x).

Groundwater gradient is calculated by the equation: i=dh/dl Where: i= groundwater gradient d= the change in, or Delta h= groundwater head l= length of casing in the well Using this you would take two wells, use the well log to determine the length (ie. depth) of each well, and subtract the first from the second. That's dl. On a particular date or time (must be the same time/date for both wells), you determine the groundwater elevations in the two wells and subtract the first from the second. That's dh. Divide dh by dl, the answer is your gradient. The gradient is dimensionless, if it's positive groundwater is flowing upward (vertically) in the direction of the first well to the second well, if it's negative, groundwater is flowing downward (vertically) in the direction of the first well to the second well.

Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.

Ang layunin ng trigonometrya ay upang lumikom ng mas maraming tumpak na sukat ng distansya bibigyan ng maliit na impormasyon tungkol sa mga anggulo o iba pang mga distansya. Ito ay ginagamit sa engineering, astronomiya, pagpaplano ng lungsod, pagbalangkas at pagdidisenyo, at construction.

The purpose of trigonometry is to gather as much accurate measurements of distances given little information about angles or other distances. It is used in engineering, astronomy, city planning, drafting and designing, and construction.

Trigonometry helps surveyors determine sides of a triangle which are either inaccessible or difficult to access. Knowing the length of a single base line enables the surveyor to define the other elements of the triangle by measuring the angle to the inaccessible points from accessible points.

Consequently the heights of trees and tall buildings can be determined by knowing the distance to the base of the tree or building. Similarly locations separated by, for example, rivers or busy roads can be determined by angular measurement from positions of known distance apart on the other side of the obstruction.

Survey control marks used for the mapping of countries were in the past established by triangulation from a known base line.

These days much of the survey control is undertaken using GPS equipment which uses satellite signals to determine positions on earth. However the theory behind the location of these positions also uses trigonometry and spherical trigonometry.

Usually it's used to find a missing angle or length of a right triangle. Of course there is more to trigonometry. Any way you can use sine, cosine, and tangent, to fine the missing angle or length

The purpose of this lesson is to review angle measures, right triangles, and the geometry of the unit circle.

Compute angles in radians and degrees and convert between the two.

Work with similar triangles.

Understand basic trigonometric functions.

Make simple computations for special angles.

The purpose of trigonometry is to gather as much accurate measurements of distances given little information about angles or other distances. It is used in engineering, astronomy, city planning, drafting and designing, and construction.