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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
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).
How do you find a slope of a line?
That depends upon what you are given - the equation of the line, the coordinates of 2 points on the line, etc.
The question does not specify the starting point.
Find the value in the equation of T plus 5 plus 3T equal 1?
T + 5 + 3T = 1
Simplify the terms, T and 3T (think 1 apple plus 3 apples)
4T + 5 = 1
Subtract 5 from both sides.
4T = -4
then divide both sides by 4 to get T by itself.
T = -4/4
T = -1
To check, substitute T = -1 wherever you see T in your original equation.
T + 5 + 3T = 1
(-1) + 5 + 3(-1) = 1
4 - 3 = 1
1 = 1 (check)
What is an expression with one variable?
3x+2 x is a variable. A variable is a symbol (x, y, etc...) that does not have an assigned value.
What is the Area of a right angled triangle?
1/2*base of triangle*height(the perpendicular)=Area of right angled triangle
A regular pentagon with perimeter 60 and apothem x. Find the area?
A pentagon has 5 sides. The perimeter is 60 so each of its sides is 60/5=12.
Area = n (s/2)^2 / tan( π /n)
= 5(12/2)^2 / tan ( π /5)
= 247.7487
What is the Formula for area of rectangle using diagonal length?
Let a, b, and c be the width, height, and diagonal of the rectangle.
Pythagorus' theorem applies to the rectangle as follows: a^2 + b^2 = c^2
substitute for 'a' from Pythagoruss theroem: a = sqrt(c^2 - b^2)
Therefore, Area = a * b = b * sqrt(c^2 - b^2) <-- we don't have enough information to solve for Area (we don't know either a or b).
Trigonometry Identity Help Express cosecant in terms of cosine?
csc(x) = 1/sin(x) = +/- 1/sqrt(1-cos^2(x))
A triangle has a degree of 180 if giving teo angles can you find the othe degree?
All triangles have angles that total 180degrees. If given 2 angles add them together and subtract (or take away from) 180, answer is angle.
Example A triangle has 2 angles of 90 & 30 degrees what is the 3rd angle. 90+30=120, 180-120=60degrees
How long has it been sine the us tried someone for piracy?
29 seconds ago. Exactly. And dude, work on your spelling!
A triangular park has sides of length 200m 155m and 172m calculate the area of the park?
The area is 12889 sq metres, approx.
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
