Mathematics, 08.01.2020 08:31 gamerdoesart

Explain why the sine of x is the sample regardless of which triangle is used to find it in the figure

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Sine of x is used when to find the side of the triangle that does not have any right angle or is not a right triangle. This is according to the Law of Sines, which states that the sides of the triangle are to one another in the ratio as the sines of their opposite angles.

Answer from: Quest

The answer is 26 to 1

Answer from: Quest

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

p1. 1 is in n.

p2. if x is in n, then its "successor" x' is in n.

p3. there is no x such that x' = 1.

p4. if x isn't 1, then there is a y in n such that y' = x.

p5. if s is a subset of n, 1 is in s, and the implication

(x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

def: let a and b be in n. if b = 1, then define a + b = a'

(using p1 and p2). if b isn't 1, then let c' = b, with c in n

(using p4), and define a + b = (a + c)'.

then you have to define 2:

def: 2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem: 1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

then 1 + 1 = 1' = 2 q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

def: let a and b be in n. if b = 0, then define a + b = a.

if b isn't 0, then let c' = b, with c in n, and define

a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

1 + 1 = (1 + 0)'

now use the first part of the definition of + on the sum in

parentheses: 1 + 1 = (1)' = 1' = 2 q.e.d.

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