Trigonometry

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.

Since there are 2 Pi radians in one complete turn, then the minute hand turns 1.75 * 2 Pi radians in 1.75 hours.

Quadrilaterals- Squares, Rectangles, Rhomboids, Parallelograms, kites, chevrons, trapezoids, and irregular quadrilaterals.

Yes, in Euclidean geometry.

The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.

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.

The double angle formula states that sin(2x) = 2sin(x)cos(x), and because sin2(x) + cos2(x) = 1, sin(2x) = 2sin(x)*SQRT(1-sin2(x)). However, that will only give you the correct result when cos(x) is positive. (because SQRT only returns the positive square root)

If, by trigonometry theorem you mean the "fundamental theorem of trigonometry," sin2(x) + cos2(x) = 1, it is actually the Pythagorean Theorem. if you have a right triangle with a hypotenuse of one, sin(x) is one leg, and cos(x) is the other. The Pythagorean Theorem states that a2 + b2 = c2 and therefore sin2(x) + cos2(x) = 1.

There is a trigonometric identity that states that sec2(x) - tan2(x) = 1, for every x. By rearranging this formula we can find that sec2(x) - 1 = tan2(x).

45 degrees

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

Thanks to the pre-existing addition and subtraction theorums, we can establish the identity:
sin(a+b) = sin(a)cos(b)+sin(a)cos(b)

Then, solving this, we get
sin(a+b) = 2(sin(a)cos(b))
sin(a)cos(b) = sin(a+b)/2

a=b, so
sin(a)cos(a) = sin(a+a)/2
sin(a)cos(a) = sin(2a)/2
Therefore, the answer is sin(2a)/2.

Let the function be f(x) = 1/(x-1)

The domain is all allowable values for which the function can be defined.

Here, except 1, any number would give the function a meaningful value. If x=1, the denominator becomes 0 and the function becomes undefined. Therefore, the domain is all real numbers except 1.

The range is all values assumed by the function.

Here, the range is negative infinity to plus infinity (that is , all real numbers).

A 9-sided "circle" is an nonagon or enneagon.