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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
Trigonometry is useful in buliding, amongst other professions and industries. Trigonometry is a branch of mathematics that deals with triangles, specifically right-angled triangles. It can be used to measure the angles of a triangle as well as all three sides, as long as two measurements are given.
Area of a trapezoid from vertices?
- Use the coordinates of the vertices to establish which two sides are parallel.
- Find the lengths of the two parallel sides (X and Y).
- Find the equation of a perpendicular to one of these lines at a point P.
- Find the point where this perpendicular line meets the other parallel line (Q).
- Find the distance PQ = H.
- Area = 1/2*(X + Y)*H
What is Squared plus 10 squared equals 12 squared?
If I have this correct you are asking x^2 + 10^2 = 12^2 Then x=6.633249507108
Find the value of sin 300 degrees?
sin 300 = -sin 60 = -sqrt(3)/2 you can get this because using the unit circle.
What is a measurement of angles?
Angles are measured by degrees. Fractions of degrees are measured in minutes and seconds.
Because it is not always convenient to convert to convert sin to cos when working with adjacent sides.
What is the cartesian system used for?
The Cartesian system allows you to describe a geometric shape in algebraic terms. This allows algebraic techniques, such as differentiation or integration to be applied to solve problems in geometry. Conversely, geometrical results can be used to solve problems in algebra.
What does an oxagon look like?
An oxagon is not a geometric shape and so does not look like anything.
What is the equation of area of a diamond?
Same as a rectangle. It is, after all, a type of rectangle (lenght >< width)
How would you explain how to find sine and cosine within each quadrant of a unit circle?
To find the sin/cos at a given point on the unit circle, draw a radius to that point. Then break the radius into components - one completely horizontal and one completely vertical. The sine is the vertical component, the cosine is the horizontal component.
If you are refering to the double-angle formula for sin(x), the best way is to use what is known as Euler's identity. Euler's identity is eix = cos(x) + i*sin(x) where x is any real angle in radians, e is Euler's constant 2.71828182845... and i is the imaginary number: SQRT(-1). Assuming that is true, then ei(2x) = cos(2x) + i*sin(2x) and that is the same as saying (eix)2= cos(2x) + i*sin(2x) and substituting from the original equation: (cos(x) + i*sin(x))2 = cos(2x) + i*sin(2x). By distribution, remembering that i2 = -1, we get cos2(x) + i*2*sin(x)*cos(x) - sin2(x) = cos(2x) + i*sin(2x). Now we can separate the equation into its real and imaginary parts. cos2(x) - sin2(x) = cos(2x) and i*2*sin(x)*cos(x) = i*sin(2x), and after i cancels, there's our good old double angle formula.
If derive refers to derivative, then use the chain rule. d(sin(2x))/dx=2cos(2x)
How long will it take a pulley rotating at 8 radians per second to make 50 complete revolutions?
(1 sec/8 rad) * (2 pi rad/1 rev) * 50 rev = 12.5 * pi seconds
about 39.27 seconds
101.6 degrees = 1.7733 radians.
So arc = radius*angle (in radians) = 219/2*1.7733 = 194.2 ft.
8.3/pi*180 is about 115. 115 is in the second quadrant.
How do you simplify csc theta cot theta?
There are 6 basic trig functions.
sin(x) = 1/csc(x)
cos(x) = 1/sec(x)
tan(x) = sin(x)/cos(x) or 1/cot(x)
csc(x) = 1/sin(x)
sec(x) = 1/cos(x)
cot(x) = cos(x)/sin(x) or 1/tan(x)
---- In your problem csc(x)*cot(x) we can simplify csc(x).
csc(x) = 1/sin(x)
Similarly, cot(x) = cos(x)/sin(x).
csc(x)*cot(x) = (1/sin[x])*(cos[x]/sin[x])
= cos(x)/sin2(x) = cos(x) * 1/sin2(x)
Either of the above answers should work.
In general, try converting your trig functions into sine and cosine to make things simpler.
X = 1st number
Y = 2nd number
Facts given:
X = 2Y (One number is equal to 2 times the second number)
2X + 2Y = 20 (2 times the 1st number, plus 2 times the 2nd number is 20)
Now we can easily find X and Y.
We'll use a method called substitution to help us.
Our first equation: X = 2Y is already solved for X. (it equals 2Y's!)
So let's substitute x = 2y into the 2nd equation and find out what y is. Remember to use parenthesis!
2x + 2y = 20
2(2y) + 2y = 20
4y + 2y = 20
6y = 20
y = 20/6
y = 10/3
We found a number for Y, even though it is a fraction.
Let's substitute it back into our 1st equation to figure out what x is.
x = 2y
x = 2(10/3)
x = 20/3
In order to check and see if x = 20/3 and y = 10/3, substitute both x and y into either equation. You pick!
2x + 2y = 20
2(20/3) + 2(10/3) = 20
40/3 + 20/3 = 20
60/3 = 20
20 = 20 (check)
Who founded analytic geometry?
People who wanted to apply complex Algebra to real world concepts, like equations of a slope on a bridge founded analytic geometry.
the angle between the two sides is used in the formula A = 1/2 a*b*sin(C) where A is area, a and b are side lengths, and C is the angle between sides. Simply use algebra to rearrange the formula to solve for C.
Express cos4x sin3x in a series of sines of multiples of x?
The best way to answer this question is with the angle addition formulas. Sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a + b) = cos(a)cos(b) - sin(a)sin(b). If you compute this repeatedly until you get sin(3x)cos(4x) = 3sin(x) - 28sin^3(x) + 56sin^5(x) - 32sin^7(x).
