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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
Heron's formula to find area of triangle
semi perimeter(s)=sum of all the sides of triangle/2
area of tiangle=P[s(s-first side)(s-second side)(s-third side)]1/2
How much does a column of water weigh if the column's height is 15 miles and its diameter is 5 feet?
pi x (2.5 ft)2 x 15 mi x 5280 ft/mi x 62.4 lb/ft3 ÷ 2000 lb/ton ≈ 48,519 tons
You sit in the sun for about 2-3-4 hours.
No! Do not sit in the sun for that long. You could get dehydrated and get sun poisioning! Use tanning lotion is the way i find most easiest OR go to a tanning bed.
Agreed, don't sit in the sun for that long- though is there even such a thing as sun poisoning?. Personally I prefer pale skin, but each to their own. If you can get a tan, sit in the sun for a little while, but drink enough water and wear sunscreen. A lot of people think this stops you from getting a tan, but it doesn't; it helps protect your skin while you get a tan. If you find getting a tan hard, you might have to get a fake tan. A tanning bed will not help if you can't get a tan normally, it will only further damage your skin.
Why are there six trigonometrics functions only?
All the trigonometric functions are derived from the right angled triangle. If we consider the three sides (AB, BC, CA) of a triangle and the included angle. There is a possibility of getting six functions based on the ratios like AB/AC, BC/AC, AB/BC, BC/AB, AC/BC, AC/AB . So we will have six trigonometric functions
What is the distance between a2 7 and b-5 0?
Dist2 = [2 - (-5)]2 + [7 - 0]2 = 72 + 72 = 2*72
So dist = 7*sqrt(2) = 9.8995
What is tan theta divided by cot theta?
Since CotΘ = 1 / tanΘ, then tanΘ / cotΘ = tanΘ / (1/tanΘ) = tanΘ x tanΘ = tan²Θ
How do you solve the questions on Circular Measure?
That depends on the questions which have not been given but in general circular measurements are:-
Circumference of a circle = 2*pi*radius or diameter*pi
Area of a circle = pi*radius2
How do you solve sin x plus cos x equals zero?
The statement of the problem is equivalent to sin x = - cos x. This is true for x = 135 degrees and x = -45 degrees, and also for (135 + 180n) degrees, where n is any integer.
How to convert degree minutes seconds angle to decimal?
Works on the same principle as "60 seconds = 1 minute and 60 minutes = 1 hour (or degree in this case)...
So for example: 2 degrees, 45 Minutes and 20 seconds is worked as follows:
Now, 20 seconds = 0.33 minutes (i.e. 20/60); add to 45 minutes to get 45.33 minutes..
45.33 minutes = 45.33/60 degrees = 0.7555 degrees.
Therefore, final answer is 2 + 0.7555 = 2.7555 degrees....
Hope this helps!!
What unit is the middle ordinate measured in?
The measurement unit depends on the characteristic that is being measured.
What is the cosine of a ratio that has 0 as its numerator?
If the numerator is 0 AND the denominator is not 0, then the ratio is 0. And cosine of 0 is 1.
Depending on which sides and angle are known you would use one of the trigonometry functions.
What does the cotangent of infinity equal?
Cotangent of ∞ is not π/2. It's actually nonexistent since cotangent is the continually oscillating function.
Express all the trigonometric ratios of cosA?
sin = sqrt(1 - cos^2)tan = sqrt(1 - cos^2)/cos
sec = 1/cos
cosec = 1/sqrt(1 - cos^2)
cot = cos/sqrt(1 - cos^2)
Can sine theta equals to theta?
Yes, it can.
If you plot theta and sin(theta) on the same graph, you will see where they intersect.
I do not know of an analytical expression for this point; I think only numerical results are possible.
What is the solution to sec plus tan equals cos over 1 plus sin?
sec + tan = cos /(1 + sin)
sec and tan are defined so cos is non-zero.
1/cos + sin/cos = cos/(1 + sin)
(1 + sin)/cos = cos/(1 + sin)
cross-multiplying, (1 + sin)2 = cos2
(1 + sin)2 = 1 - sin2
1 + 2sin + sin2 = 1 - sin2
2sin2 + 2sin = 0
sin2 + sin = 0
sin(sin + 1) = 0
so sin = 0 or sin = -1
But sin = -1 implies that cos = 0 and cos is non-zero.
Therefore sin = 0 or the solutions are k*pi radians where k is an integer.
How do you derived the sine law?
Consider any triangle ABC, and let AD be the altitude from A on to BC.
Then sin(B) = AD/AB so that AD = AB*sin(B)
and sin(C) = AD/AC so that AD = AC*sin(C)
Therefore AB*sin(B) = AC*sin(C)
or c*sin(B) = b*sin(C) where the lower case letter represents the side opposite the angle with the upper case name.
Divide both sides by bc to give sin(B)/b = sin(C)/c.
Similarly, using the altitude from B you can show that sin(A)/a = sin(C)/c.
Combining with the previous result,
sin(A)/a = sin(B)/b = sin(C)/c.
