0
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
How do you find exact value without calculator?
sine tables, that's how they did it before calculators, there are formulas as well
How do you calculate the sides of a parallelogram given the height and longer diagonal?
The height and longer diagonal do not provide enough information to calculate the sides.
When is sin x equal to cos x times cos x?
To figure this out, graph y = sin x and y = cos2 x on the same piece of paper or graphing utility and find the points where the graphs intersect.
To determine this analytically, take the equation sin x = cos2 x and divide both sides by cos x to obtain the equivalent expression tan x = cos x. What this means is that the ratio of the opposite side of the triangle formed by angle x and the triangle's adjacent side is equal to the ratio of the triangle's adjacent side divided by its hypotenuse. This can be expressed by using the variables x and y to represent the opposite side and the adjacent side, respectively, by the expression
x2/y2 = y2/(x2 + y2)
where x2 + y2 equals the hypotenuse squared and x2/y2 equals the tangent squared. Now you can solve for either y or x by plugging in any number into the other (here we will solve for x by plugging 1 into y to obtain the expression
x2 = 1/(x2 + 1)
This can be rearranged to the form
x4 + x2 - 1 = 0
We can now solve for x2 using the quadratic formula.
[-1 + or - (1 + 4)1/2]/2
This equals negative one plus or minus the square root of five, all divided by two. Since we need to find the square root of x2, and negative numbers don't have real square roots, and negative one minus the square root of five divided by two is negative, we shall take the square root of negative one plus the square root of five divided by two, since this yields a real value. This approximately equals 0.6180. This, divided by our chosen y value, is the tangent of all angles for which the sine equals the cosine squared, and since our chosen y-value is 1, we can simply use a calculator's tan-1 function to find the value within the domain 0 x = 31.7175 + 180n where n is any integer, positive or negative.
It is necessary to mention that the two triangles are similar.
Let the perimeter of the triangle MNP be x cm.
Since the triangles XYZ and MNP are similar triangles,
8/12 = x/80 (multiply both sides by 80)
640/12 = x
53.3333... = x
53 3/9 = x
53 1/3 = x
Thus, the perimeter of the triangle MNP is 53 1/3 cm.
Is the cosine sine and tangent of an angle equal to each other?
No; those could be three different values, or sometimes two of them might be the same. For example, if the angle is 45 degrees, the values are about...
cos:0.707
sin: 0.707
tan: 1
For 45 degrees, the cosine and sine are the same. For 36 degrees,
cos:0.809
sin: 0.588
tan: .727
Where did the word Phoenix come from?
(taken from wikipedia)
The Greeks adapted the word bennu and identified it with their own word phoenix φοινιξ, meaning the colour purple-red or crimson. They came up with the word Phoenicia.
(added)
The Phoenicians traded a purple-red dye of the same name. The people were named for the dye that they traded.
and it also is a Persian myth .. which they call it ققنوس .
What is the measurement for which the sine is at its maximum?
It is pi/2 + 2*k*pi radians for integer k.
What is the difference between proof and postulate?
A proof uses postulates and theorems to prove some statement.
What is the minimum number of triangles required to triangulate an hendecagon?
9 (two less than the number of vertices in the polygon).
What is the equation of a circle whose center is at the origin and whose radius is 16?
(x-0)² + (y-0)² = r²
What is function and relation?
All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.
Which two trigonometric functions are used for analyzing vectors?
You usually need all three primary functions.
The sine and cosine functions are used to resolve the vector along orthogonal axes, and the tangent function is used to find its direction.
How do you draw a perfect circle?
Get a cup or bottle somethig round orrr... you can stick a hole in the middle with a thumbtack in it with string on the thubtack conected to the pen (or pencil) and go around:)
The cosine of 10 degrees is 0.9848, approximately. The cosine of 10 radians is roughly -0.8391
Can someone verify that sec4 theta-sec2 theta equals tan4 theta plus tan2 theta?
sec4(Θ) - sec2(Θ) = tan4(Θ) + tan2(Θ)
Factor each side: sec2(Θ) [sec2(Θ) - 1] = tan2(Θ) [tan2(Θ) + 1]
Use the identitiy: 1 + tan2(Θ) = sec2(Θ)
We can also write it as: tan2(Θ) = sec2(Θ) - 1
Substitute the first form of the identity in the right side: sec2(Θ) [sec2(Θ) - 1] = tan2(Θ) sec2(Θ)
Substitute the second form of the identity in the left side: sec2(Θ) tan2(Θ) = tan2(Θ) sec2(Θ)
Is that close enough for you ?
Is it worth a trust point ?
