Trigonometry

An equilateral triangle has 3 equal sides and 3 equal 60 interior angles that add up to 180 degrees

Whenever architecture involves the use of lines that are not on the x or y axis, it will involve trigonometry to calculate the length of lines and the angles they make from one another.
One example is calculating roof pitch.

8pi/9

They are classified as: scalene, obtuse, right angle. equilateral and isosceles

12.0 if you want 3 sig-figs, or 12 if you only want 2.

There are four quadrants. They are represented by Roman numerals : I(one), II(two), III(three), IV(four). The first quadrant contains all positive points , (+x, +y) The second quadrant contains negative x's and positive y's , (-x, +y)

The third quadrant is all negative , (-x, -y)

The fourth quadrant has negative y's and positive x's , (+x, -y)

Just add together the 4 sides

Same as a rectangle. It is, after all, a type of rectangle (lenght >< width)

sin 300 = -sin 60 = -sqrt(3)/2 you can get this because using the unit circle.

Angles are measured by degrees. Fractions of degrees are measured in minutes and seconds.

Cos is the ratio between adjacent side (of the given angle thieta) to the hypotenuse of the triangle.

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)

Yes, in Euclidean geometry.

ADDING: same sign, add and keep that sign. opposite sides, subtract their absolute values and use the sign of the number with the larger absolute value

SUBRTRACTING: change the sign of the subtrahend (2nd number) then ADD using rules above.

(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.

in trigonometry

Because it is not always convenient to convert to convert sin to cos when working with adjacent sides.

The Tangemt Formula for Geometry is opposite over adjacent, or opp./adj.

It depends on what else you know about the triangle.

Maybe a parallelogram. You should do a google image search for parallelogram and see if it's the shape you're thinking of.

A hectagon has 100 sides. It might be confused with a heptagon which has 7 sides.