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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

What is the smallest angle of a triangle with sides of 6.4 cm 8.2 cm and 5.7 cm?

The smallest angle will be opposite the smallest side of the triangle and so by using the cosine rule it works out as 43.84 degrees.

What is the rule of trigonometry?

Just remember SOHCAHTOA,

SOH is using the sine, only use this when you have the Hypotenuse and the Opposite.

Sin(a)= O/H

CAH is using the cosine, only use this when you have the Hypotenuse and Adjasent.

Cos(a)=A/H

TOA is using the tangent, only use this when you have the Opposite and Adjasent.

Tan(a)=O/A

Is a tangent a trigonometric ratio?

Tangent is used in calculus to compute the slope of a curve. Because curves do not have uniform slopes, unlike lines, their slopes change. A tangent is the slope of a curve at a specific point.

What are the different of congruent triangle and similar triangle?

The corresponding angles in both cases are the same. With congruent triangles, the lengths of the corresponding sides are also equal.

If a triangular prism has a length 10m and volume 180 cu m what are two possible integer height and widths?

180/10 = 18 square meters of cross-sectional area.

Since the prism is a triangle, that means that the height x width = 36, since A = (H*W)/2

Therefore you could say 6x6, 18x2, 4x9, or even 36x1.

How do you figure out the bearing point in trigonometry in math?

You find the angle with a fixed direction using trigonometry. You then convert it to an angle measured in degrees, clockwise from North, and written as a three digit number.

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.