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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 does sin(pi/4) = ?
Let's consider a special right triangle: the 45-45-90 triangle.
In any 45-45-90 triangle, since the two 45 degree angles are congruent, the sides opposite to those angles are both congruent.
Now, considering the unit circle, the radius of the circle must be one.
So, if you put in a 45-45-90 triangle in a unit circle, this allows you to find the value of sin pi/4 because pi/4 radians = 45 degrees.
Because the circle has radius 1, the hypotenuse of the triangle must also be one. Since the other two sides must be equal, you can solve for them using the Pythagorean theorem.
a2 + b2 = c2
a2 + a2 = 12
2a2 = 1
a2 = 1/2
a = √(1/2)
a = 1/√(2) * (√(2)/√(2))
a = √(2) / 2
Since sin is defined as opp/hyp, sin 45 degrees (pi/4 radians) = (√(2)/2)/1 = √(2)/2
I hope this helped explain my answer. If there's anything that's still confusing, just tell me. (Sorry I didn't do it the first time).
Sin(20) =
You need either a scientific calculator or Castles four figure Tables.
Using a scientific calculator
Sin ( 20 ) = 0.342020143....
Sin(20) ~ 0.3420 (4d.p.).
What is a ten-sided figure called?
A ten sided figure is called a Decagon. ( i think that's how you spell it. )
ArcTan is another name for ;Inverse Tan' or 'Tan^*-1)
Hence
ArcTan(0.55431) = 29.00004157 degrees.
Effectively 29 degrees.
4Sin(x)Cos(x) =
2(2Sin(x)Cos(x)) =
2Sin(2x) ( A Trig. identity.
What is the turning point in the graph of a quadratic function?
The answer depends on the form in which the quadratic function is given.
If it is y = ax2 + bx + c
then the x-coordinate of the turning point is -b/(2a)
P(First card) = 13/52
P(second card = 12/51 Because you have already drawn one spade , there is one less card in the pack .
P(Both spades) = 13/52 X 12/51 = 156/2652 = 0.0588
Cos(2A) = Cos(A + A)
Double Angle Indentity
Cos(A+A) = Cos(A)Cos(A) - Sin(A)Sin(A) =>
Cos^(2)[A] - SIn^(2)[A] =>
Cos^(2)[A] - (1 - Cos^(2)[A] =>
2Cos^(2)[A] - 1
On a calculator type in 'Sin' , followed by '30' follwed by '=' . The answer is '0,5'.
Sin(30) = 0.5
All the trig. values are based on a triangle integrated into a circle.
Practically,
On a piece of graph paper, draw a circle centred on the origin (0,0).
Call the radius of that circle '1'.
Now draw a radius 30 degrees from the x-axis.
Then drop a line from point on the circle were the radius meets( intersects) the circle. to the x-axis, to meet the x-axis at 90 degrees. This 'dropped' line is the 'opposite' to the angle 30 degrees. Measure the length of this 'dropped'; line. You will find it to be exactly half (0.5 = 1/2) the length of the radius.
Similarly, if the radial angle is 45 degrees a corresponding sine value is 0.707106781... = sqrt(2)/2 = 1/sqrt(2).
All other 'Sine' values can be found in a similar manner. However, to save time on drawing circles and triangles, the trig. values are integrated into modern calculators or formerly into Castle's Four Figure Tables.
This is NOT a Pythagorean triangle.
So we must fall back on the Cosine Rule for an agular value.
Cosine Rule is a^(2) = b^(2) + c^(2) - 2bcCosA
Algebraically rearranging
CosA = [a^(2) - b^(2) - c^(2)] / -2bc
Substituting
CosA = [10^(2) - 7^(2) - 5^)2)] / -(2(7)(5))
CosA = [100 - 49 - 25]/-70
CosA = 26/-70
CosA = -0.371428571...
A = Cos^(-1) -0.371428573
A =111.8037 481 ... degrees. -
Now area of triangle is 0.5 X Base X height
The height is = 7Sin(111.8037481...)
Hence are is 0.5(5)(7)Sin(111.8037481...)
Area = 16.248... m^(2)
Is arc of a circle a undefined term?
The Arc of a circle is that part of the circumference between two radii.
What is angle Theta if sine theta 0.03125?
Sin(theta) = 0.03125
Hence
theta = ArcSin(0.03125)
theta = 1.790784659... degrees.
What is the other name of trigonometry?
There is no other names!!!!
Howver 'the word' trigonmetry' comes from Latin, and means 'measuring triangles.'.
trigon ( a three sided 2-dimenstional figure) = triangle (modern).
Metry = to measure.
Solution for tan x is equal to cos x?
Tan(x) = Sin(x) / Cos(x)
Hence
Sin(x) / Cos(x) = Cos(x)
Sin(x) = Cos^(2)[x]
Sin(x) = 1 - Sin^(2)[x]
Sin^(2)[x] + Sin(x) - 1 = 0
It is now in Quadratic form to solve for Sin(x)
Sin(x) = { -1 +/-sqrt[1^(2) - 4(1)(-1)]} / 2(1)
Sin(x) = { -1 +/-sqrt[5[} / 2
Sin(x) = {-1 +/-2.236067978... ] / 2
Sin(x) = -3.236067978...] / 2
Sin(x) = -1.61803.... ( This is unresolved as Sine values can only range from '1' to '-1')
&
Sin(x) = 1.236067978... / 2
Sin(x) = 0.618033989...
x = Sin^(-1) [ 0.618033989...]
x = 38.17270765.... degrees.
What is the value of theta if 4sin theta is equal to 2?
4Sin(theta) = 2
Sin(Theta) = 2/4 = 1/2 - 0.5
Theta = Sin^(-1) [0.5]
Theta = 30 degrees.
What trig function has a value of 1?
Sin(90)= 1.000
Cos(0) = 1.000
Tan(45) = 1.000
NB The angular values repeat every 360 degrees.
The value of cos 46 degrees is approximately 0.7193. Cosine is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, when the angle is 46 degrees, the cosine value is calculated by dividing the length of the adjacent side by the length of the hypotenuse.
What is the sum of the first 100 odd numbers?
Oh honey, the sum of the first 100 odd numbers is 10,000. You see, the formula for the sum of the first n odd numbers is n^2, and since 100 is the 50th odd number, 50^2 equals 10,000. So, there you have it, darling.
What is the csc of a 63 degree angle?
Well, darling, the cosecant (csc) of a 63 degree angle is simply 1/sin(63). So, grab your calculator and divide 1 by the sine of 63 degrees to get your answer. Math doesn't have to be a drag, honey!
How do Round 10.9 to 1 decimal place?
Well, honey, to round 10.9 to 1 decimal place, you just look at the digit right after the decimal point. If it's 5 or greater, you round up. So, 10.9 rounded to 1 decimal place is 11. Easy peasy, lemon squeezy!
What is the third square root of 216?
Do you mean (((216^(1/2))^(1/2))^(1/2)) or [216^(1/2)] / 3
The first answer is 216^(1/8) = 1.957973....
The second one is 216^(1/2) / 3 = 4.898979486....
