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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 are the double-angle and half-angle identities?

sin 2θ = 2(sin θ)(cos θ)

cos 2θ = (cos θ)2 - (sin θ)2

cos 2θ = 2(cos θ)2 - 1

cos 2θ = 1 - 2(sin θ)2

tan 2θ = 2(tan θ)/[1 - (tan θ)2]

sin θ/2 = ±√[(1 - (cos θ))/2]

cos θ/2 = ±√[(1 + (cos θ))/2]

tan θ/2 = ±√[(1 - (cos θ))/(1 + (cos θ))] ; cos θ ≠ -1

tan θ/2 = [1 - (cos θ)]/(sin θ)

tan θ/2 = (sin θ)/[1 + (cos θ)]

Does a triangular prism has 3 rectangular faces?

Short answer, yes.

Long answer, a triangular prism has two triangular faces, its bases, and three rectangular faces, its sides, which connect the two faces. Unfolding the prism into a net reveals a rectangle divided into three rectangular sections (these are the three rectangular faces) and two congruent triangles attached along a common edge to one of these rectangles (these are the two triangular faces).

What is cotangent of 270 degrees?

Firstly, with the unit circle (r=1) we need to know that:

at 270 degrees our coordinates are (0, -1)


sine(270 degrees) = -1

cosine(250 degrees) = 0


cotangent = cosine / sine

therefore: cot ( 270 degrees) = 0/-1 = 0


The answer is 0.

How do you simplify cosx plus sinx tanx?

to simplify Cosx=Sinx Tanx you should remember your fundamental and pythagorean identities..

Cosx + Sinx Tanx

Cosx + Sinx (Sinx/Cosx) <---------- From Tanx= Sinx/Cosx

Cosx + Sin2x/ Cos x <------------- do the LCD

Cosx (Cosx/Cosx) + Sin2x/Cosx

(Cos2x+Sin2x)/Cosx

1/Cosx <--------- From Sin2x + Cos2x =1

or Secx <-------- answer

Comment if you have questions...:))

How do you confirm this trig identity?

sin^5 2x = 1/8 sin2x (cos(8x) - 4 cos(4x)+3)

What is a 213 degree angle?

An angle of 213 degrees is a reflex angle

What jobs use trigonometry functions?

Often people involved in industrial production will use polar graphs to program their machines; take, for, example, a pretzel-making machine. They can graph the path the "dough-shaping" machine must follow on a polar graph.

What is the triangular prism volume formula?

The Formula is Base*Height, or 1/2 Height (altitude of the triangle) * Base (of the Triangle) * height (Height of the prism)

What is the probability that a couple with 3 children will have at least 1 girl?

The easiest way of calculating this is to find the probability that all three are boys, as this is the only arrangement that does not fit the criteria. Then work out the answer by taking this away from 1. Probability that all three are boys = 1/2 x 1/2 x 1/2 = 1/8. probability of there being at least one girl is 1 - 1/8 = 7/8 or 87.5%

Why the value of tan A is always less than one?

The values of tan are limitless (that is to say, within [-inf, inf]). However, sin and cos ratios are between -1 and 1. Think about it: sin = opposite/hypotenuse. Since hypotenuse is always larger than or equal to opposite, sin must always be less than 1. Same with cos.

What is The Latin maxim nulla poena sine lege is also known as?

The principle of legality; no act should be made criminal or punished without advance warning in the form of legislative act.

How do you find the hypotenuse of a right triangle when only a side length and angle is given?

Dependent on what side you are given you would use Sin(Θ) = Opposite/Hypotenuse just rearrange the formula to Hypotenuse = Opposite/Sin(Θ).

Or if you are given the adjacent side use Cosine(Θ)=Adjacent/Hypotenuse, then:

Hypotenuse = Adjacent/Cosine(Θ)

Where is the origin of trigonometry in 18Th century?

The origin of trigonometry in the 18th century was the trigonometric knowledge at the end of the 17th century!