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Trigonometry

Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.

3,810 Questions

A car coasts engine off up a 30 degree grade if the speed of the car is 25 meters per second at the bottom of the grade what is the distance traveled by the car before it comes to rest?

At the bottom, the car has kinetic energy of ½mv2. At the top, the car has kinetic energy of 0. If we ignore friction and wind resistance, the initial kinetic energy is converted to gravitational potential energy of mgh, where the m is again the mass of the car, g is the acceleration of gravity, and h is the vertical change in position of the car. Solving the two equations for h, we get

h=½v2/g=(0.5)(25 m/s)2/(9.8 m/s2)=31.888 m

To find the distance traveled along the road, we use a bit of trigonometry: sin(30°) = h/d = 0.5, so d = 2h = 63.776 meters

Of course, the actual value will be less, due to the friction and wind resistance that we ignored in our calculations.

What are the applications of the field?

The answer depends on the context. The applications will vary from one context to another.

There are agricultural fields.

There are vector fields in physics which depict the magnitudes and directions of forces.

There are algebraic structures called fields which have some mathematical properties associated with them.

What is the definition for a point as in geometry?

The specific location of something or in which something is occurring or has happened, or the measurement of something that happened or is happening is a point in geometry.

How many mils are there in one revolution?

There can be no equivalence.

A mil is a measure of length or linear displacement while a revolution is a measure of angular displacement. The two measure different things and, according to basic principles of dimensional analysis, any attempt at conversion from one to the other is fundamentally flawed.

Is trigonometry included in order of operations?

Not specifically trigonometry, but functions in general. As a general rule, functions must be evaluated before using the results in other parts of the calcuation.

What is the identity for tan theta?

The identity for tan(theta) is sin(theta)/cos(theta).

Definition of ogive diagram?

An ogive is a type of graph that is used to represent the cumulative frequencies for the classes in a frequency distribution. This type of graph can also be known as a cumulative frequency graph. The cumulative frequency is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution.

How is pi related to trignometry?

The angles of a triangle sum to pi radians, or the angles at a point sum to 2*pi radians.

Why is the period of a function important when solving a trig equation?

there can be more than 1 answer for some trig equations and you must use your knowledge of periodicity to get the answers.

What is the height of the hill if the elevation of a hill at a place due east of it is 39 degrees at a place B due south of A the elevation is 27 degrees and the distance from A to B is 500m?

It is not clear from the question where the point A is. This answer assumes that A is the point to the East of the hill.

Suppose the height of the hill is h metres. Suppose O is the point, on ground level, under the apex of the hill.

Then tan(39) = h/OA so that OA = h/tan(39)

Also tan(27) = h/OB so that OB = h/tan(27)

Now, triangle OAB has a right angle at A,

so by Pythagoras, OB2 = OA2 + AB2

Therefore h2/tan2(27) = h2/tan2(39) + 5002

that is h2/0.2596 = h2/0.6558 + 250000

so that 2.3269h2 = 250000

h2 = 107441

h = 327.8 metres.

1 minus 2 cosine squared divided by sine cosine is equal to tangent minus cotangent?

No, it is not. To be correct, the expression requires parenthesis, which are missing.

What is the purpose of trigonometry in the fields of surveying navigations engineering and other branches of physical sciences?

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.

What does sin stand for?

Sin is a math abbreviation for sine a trigonometry function

or

It is a religions term that is the act of violating a moral law or code.

see related links for more information of both

What is a True compass bearing?

The definition of a true compass bearing - A true bearing is measured in relation to the fixed horizontal reference plane of True North, that is using the direction towards the geographic North Pole as a reference point.

Who are the leaders in Twelve Angry Men?

Well, there really are no leaders in Twelve Angry Men, but those with more 'input' would include Juror #1 (Martin Balsam) the Foreman and Juror #8 (Henry Fonda) who pushes for fellow jury members to consider the possibility the Defendant may not be guilty of the crime.

By using trigonometric identities find the value of sin A if tan A equals a half?

If tan A = 1/2, then sin A = ?

We use the Pythagorean identity 1 + cot2 A = csc2 A to find csc A, and then the reciprocal identity sin A = 1/csc A to find sin A.

tan A = 1/2 (since tan A is positive, A is in the first or the third quadrant)

cot A = 1/tan A = 1/(1/2) = 2

1 + cot2 A = csc2 A

1 + (2)2 = csc2 A

5 = csc2 A

√5 = csc A (when A is in the first quadrant)

1/√5 = sin A

√5/5 = sin A

If A is in the third quadrant, then sin A = -√5/5.