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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 ratio correctly describes the cosine function?

The cosine of theta is adjacent over hypotenuse, given a right triangle, theta not being the 90 degree angle, adjacent not being the hypotenuse, and theta being the angle between adjacent and hypotenuse.

In a unit triangle, i.e. in a unit circle circumscribed with radius one, and theta and the center of the circle at the origin, cosine of theta is X.

The given angle is 1291 degrees what terminal quadrant does it lie in?

3rd quadrant. The four 90 degree quadrants together formed 360 degrees. When a given angle is greater than 360 degrees, subtract 360 from it till a value smaller than 360 is obtained. In this way, we can determine the quadrant in which the given angle lies. Here the final angle obtained is 211 degrees (1291-3x360=211).

Do I need to learn algebra before trigonometry?

YES! If you can't do algebra, you won't last ten seconds in trigonometry. It basically is algebra, just using equations within equations.

How do you simplify sin theta times csc theta divided by tan theta?

Since sin(theta) = 1/cosec(theta) the first two terms simply camcel out and you are left with 1 divided by tan(theta), which is cot(theta).

What is the formula for the angular velocity?

There are several, what is it that you want to calculate?

The "natural" units for angular velocity are radians/second. The relationship between linear velocity and angular velocity is especially simple in this case: linear velocity (at the edge) = angular velocity x radius.

Evaluate the following without a calculator and leave in radical form cos 90 sin 270?

First draw the graph.

Label A S T C according to the order of plane.

Draw a 90 degree angle.

You see it's between All and Sin, so the answer is 0

Draw 270 degree angle.

You see it's between Tan and Cos, so the answer is -1

And when you mix them together, 0 times -1 = 0.

How do i simplify csc theta divided by sec theta?

By converting cosecants and secants to the equivalent sine and cosine functions. For example, csc theta is the same as 1 / sin thetha.

What is the answer of csc x plus cot x?

Without an "equals" sign somewhere, no question has been asked,

so there's nothing there that needs an answer.

Is it the sum that you're looking for ?

csc(x) + cot(x) = 1/sin(x) + cos(x)/sin(x) = [1 + cos(x)] / sin(x)

How does the military use trigonometry?

It is used to calculate the trajectories of projectiles and missiles.

What does 2sin squared theta equal and why?

It is 2*sin(theta)*sin(theta) because that is how multiplication is defined!

What is cos of 2 theta?

cos(A + B) = cosAcosB - sinAsinB, with A=B, cos(2A) = cos2A - sin2A, then you can use cos2A + sin2A = 1, to produce more, like: [2cos2A - 1] or [1 - 2sin2A], and others.

What is the cosine of phi?

phi = [(1+sqrt(5)]/2 = 1.6180, the golden ratio.

cosine(phi) = -0.0472 approx.

True or False y equals sin theta is not a function because sin 30 degrees equals sin 150 degrees. Justify your answer?

False.

A function can map several (or even all) values in the domain to a single value in the range. What it cannot do, is to map a single value in the domain to several values in the range. In other words, a function can be many-to-one (or one-to-one) but not one-to-many.


One consequence of sin30 = sin150 is that arcsine is not a function unless its range is restricted to -90 to +90 degrees - or some equivalent interval.



Which function's graph has a period of 2?

There are an infinite number. The simplest is a sinusoid. The sine function has period 2π, so you compress it by a factor of π: f(x) = sin (πx).

What are the solutions of 2 cos squared x minus cos x equals 1?

2cos2x - cosx -1 = 0

Factor:

(2cosx + 1)(cosx - 1) = 0

cosx = {-.5, 1}

x = {...0, 120, 240, 360,...} degrees

What is the third square root of 0.125?

It is not clearly mentioned that whether it is the "THIRD" root we have to calculate.. or the "SQUARE ROOT THREE TIMES.. i.e the EIGHTth ROOT".. The answer posted here before was not correct in a sense that the if the question demands "third square root" which can also mean the "EIGHTth" root..

Re-edit:

It seems rather obvious that this answerer is new to wiki answers and is not in the habit of question interpretation. The question is most likely thus; " What is the cubic root of 0.125. The answer then would be...,

cubic root(0.125)

= 0.5

====( calculate the square root three times?!? sounds like a stretched interpretation )

Do you know what square root means? -_- if u know.. then u clearly know what "third square root means" .. huh -_-