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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 largest Pythagorean Triple?
There is no largest Pythagorean triple since there's infinite amount of them. But if you're looking for one quite big, I took a few minutes for you and wrote a program that computes them (and btw is still computing them). Right now the largest one the function returned is 77893200, 128189952, 150000048. Note that you can multiply all three with any same natural number larger than one (2,3,4,...) and you'll get a Pythagorean triple larger than mine.
What is the law of trigonometry?
There is no single law in trigonometry so the question makes no sense.
How do you find the elevation of the sun?
WARNING: Do not, under any conditions, look at the sun, directly or indirectly.
The find the elevation of the sun, measure the angle that an object's shadow from the sun makes. One way to do this is with a stick in the ground. Assuming the stick is perpendicular to the ground, the ratio of the stick's length to the shadow's length is the tangent of the angle of elevation. Solve for inverse tangent, and you have the angle.
Show that cos3t equals 4cos cubed t - 3cos t?
cos(3t) = cos(2t + t) = cos(2t)*cos(t) - sin(2t)*sin(t)
= [cos2(t) - sin2(t)]*cos(t) - 2*cos(t)*sin(t)*sin(t)
= [cos2(t) - sin2(t)]*cos(t) - 2*cos(t)*sin2(t)
then, since sin2(t) = 1 - cos2(t)
= [2*cos2(t) - 1]*cos(t) - 2*cos(t)*[1 - cos2(t)]
= 2*cos3(t) - cos(t) - 2*cos(t) + 2*cos3(t)
= 4*cos3(t) - 3*cos(t)
What is the area of an irregular figure-sides 2cm 3cm 4cm and 9cm?
2X3=6+(4X9)=
42
42 square centimeters
Average Rate of Change Fx equals x2 plus 3x plus 5.1 from x1 equals -5 to x2 equals 6?
f(x1) = (-5)2 + 3*(-5) + 5.1 = 25 - 15 + 5.1 = 15.1
f(x2) = (6)2 + 3*(6) + 5.1 = 36 + 18 + 5.1 = 59.1
f(x2)-f(x1) = 59.1 - 15.1 = 44
x2 - x1 = 6 - (-5) = 11
So average rate of change = 44/11 = 4
What is Cos 2 x divided by cos x?
cos 2x = cos2 x - sin2 x
= 2 cos2 x - 1; whence,
cos 2x / cos x = 2 cos x - (1 / cos x)
= 2 cos x - sec x.
Round the base angle to 70 degrees and use the sine ratio:
30*sine 70 degrees = 28.19077862 feet
Height of ladder from the ground = 28 feet to 2 s.f.
Is a triangle with sides of lengths 20 21 and 29 a right triangle?
Yes.
Using Pythagorean's theorem: 202+212 = 400+441 = 841 = 292 = 841
2sinx - sin3x = 0
2sinx - 3sinx + 4sin3x = 0
4sin3x - sinx = 0
sinx(4sin2x - 1) = 0
sinx*(2sinx - 1)(2sinx + 1) = 0
so sinx = 0
or sinx = -1/2
or sinx = 1/2
It is not possible to go any further since the domain for x is not defined.
What natural phenomena are the basis for time measurements?
scientists use an atom of helium and look at the # of rotations of the electrons around the nucleus. and they determine the second from that
How do you find the measure of an angle by using its tangent?
You would have to use its opposite tangent, tan-1on your scientific calculator. It would be tan-1(opposite side/adjacent side), and you must have the opposite and adjacent sides of the angle you are trying to solve.
If sinX plus cosecx equals 2 find sin40x plus cosec50x?
sin x + csc x = 2
sin x + 1/sin x = 2
(sin2 x + 1)/sin x = 2/1 (cross multiply)
sin2 x + 1 = 2sin x (subtract 2sin x to both sides)
sin2 x - 2sinx + 1 = 0
(sin x - 1)2 = 0 (take the square root of both sides)
sin x - 1 = 0 (add 1 to both sides)
sin x = 1
x = sin-1 1 = 90⁰
40x = 40(90⁰) = 3,600⁰
sin 40x = sin (3,600⁰ ) = 0
50x = 50(90⁰) = 4500⁰
sin 50x = sin (4,500⁰) = 0, so that csc 50x is undefined, we cannot divide by 0.
Then, sin40x + csc50x is undefined.
What is the exact value answers in degrees of two cos x minus radical three equals zero?
30 degrees
explanation
2Cosx-radical 3=0
Then 2cosx=radical 3
and cos x=(radical 3)/2
Now remember that cos 300 is (radical 3)/2 from the 30/60/90 triangle.
So the answer is 30 degrees.
What are the zeros in sine and cosine function?
A "zero of a function" is a point where the dependent value (usually, Y) is zero. In the function f(x) = x2 - 2, for example, there are zeroes at -1.414 and +1.414.
The zeroes of the sine function are at all integer multiples of pi, i.e. 0, pi, 2pi, 3pi, etc. The zeroes of the cosine function are at the same points plus pi/2, i.e. pi/2, 3pi/2, 5pi/2, etc.
Another way to look at this is that the zeroes of sine are the even multiples of pi/2, and the zeros of cosine are the odd multiples of pi/2.
Composite figures of right triangles in trigonometry?
A composite figure is a figure that is made up of several smaller geometric figures like triangles, circles, or rectangles.
In a right angle triangle it is:
cosine ratio = adjacent/hypotenuse
Rectilinear figures are figures that are produced using just line segments. All of the polygons are rectilinear figures and many 3-dimensional solid shapes are as well.
