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

Think of tangent as sin divided by cos or sin/cos. Now cos 90 degrees is 0 so tan90 would be 1/0 which is not define since you are now allowed to divide by 0. It's best to visualize what Tan(90) means: Take a typical right angle triangle: From the angle in question (A), you have the adjacent leg (The leg extending from angle A to the right angle opposite), the opposite leg (the leg directly opposite the angle A, of course) and the hypotenuse (the leg intersecting the aforementioned two legs) Tan(A) is the ratio of the opposite leg and the adjacent leg. To solve for Tan (A): Tan (A) = opposite/adjacent. As angle (A) increases, the length of the opposite side also increases. So what happens at A=90? Well, you no longer have a triangle! The hypotenuse (the leg that intersects the opposite side from the adjacent side) NEVER INTERSECTS. Therefore, no longer being a triangle, you can no longer define the ratio.

If none of the letters were repeated, the answer would be 7!. However, the letters M & E are repeated. So, we need to divide the 7! by 2! twice to account for the two letters repeated twice. The solution is: 7! / (2! * 2!). This written out is: (7*6*5*4*3*2*1)/(2*1*2*1) or 1260.

The circumference of a circle C is 2Pixr So solving for r we have C/2Pi=r

If sin θ = tan θ, that means cos θ is 1 (since tan θ = (sin θ)/(cos θ))

(Usually in and equation a/b=a, b doesn't have to be 1 when a is 0, but cos θ = 1 if and only if sin θ = 0)

The angles that satisfy cos θ = 1 is 2n(pi) (or 360n in degrees)

When n is an integer.

But if sin θ = tan θ = θ, the only answer is θ = 0.

Because sin 0 is 0 and cos 0 is 1 and tan 0 is 0

The only answer would be when θ = 0.

Cosine squared theta = 1 + Sine squared theta

If x2 + y2 = 1, then the point (x,y) is a point on the unit circle.

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A Quadrantal angle is an angle that is not in Quadrant I. Consider angle 120. You want to find cos(120) . 120 lies in quadrant II. Also, 120=180-60. So, it is enough to find cos(60) and put the proper sign. cos(60)=1/2. Cosine is negative in quadrant II, Therefore, cos(120) = -1/2.

It is 3 minus 2i

Acute angles (less than 90 degrees)

Obtuse angles (greater than 90 degrees)

Right angles ( equal to 90 degrees)

The trigonometric functions are sine, cosine and tangent along with their reciprocals and the inverses. Whether the angle is acute or obtuse (or reflex) makes no difference).

The related link shows a set of complex numbers that depict the Electro-Magnetic

fields around two wires. The formula is (z-1)/(z+1)

The point of origin is not in any quadrant. In fact, any point on the X or Y axis is not in a quadrant. In order for a point to be in Q1, Q2, Q3 or Q4, it must not be on an axis.

area=(1/2)*base*height

No. A circle has no straight lines. You can approximate circles with very small straight lines (that's how a computer draws circles) but mathematically, no.

It is a legal term that refers to an act that causes damage but without infringing any legal rights.

For example, if you have a shop and I open a shop selling identical goods next door, I will probably damage your business but I will not have infringed your legal rights - unless you have some exclusivity arrangement.

cotA*cotB*cotC = 1/[tanA+tanB+tanC]

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

Yes. Trigonometric identities are extremely important when solving calculus equations, especially while integrating.

It depends on what else you know about the triangle.

If you know two sides of a triangle, trig lets you find the third. So if you want to know the distance across a lake, measure two lines along the side of the lake such that they form a triangle with the line across the lake, and you can find the distance across. You can also find one side if you know one side and the angles at either end. This can be used to find the heights of objects - you know the angle it makes to the ground, how far you are from it, and what angle you have to look at to see the top.

The width of a ball is its diameter, so the diameter of a ball that is 24 cm wide is 24 cm.