Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"
A polynomial can have:
constants (like 3, −20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed
that can be combined using addition, subtraction, multiplication and division ...
... except ...
... not division by a variable (so something like 2/x is right out)
So:
A polynomial can have constants, variables and exponents,
but never division by a variable.
Also they can have one or more terms, but not an infinite number of terms.
These are polynomials:
3x
x − 2
−6y2 − ( 79 )x
3xyz + 3xy2z − 0.1xz − 200y + 0.5
512v5 + 99w5
5
(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)
These are not polynomials
3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
2/(x+2) is not, because dividing by a variable is not allowed
1/x is not either
√x is not, because the exponent is "½" (see fractional exponents)
But these are allowed:
x/2 is allowed, because you can divide by a constant
also 3x/8 for the same reason
√2 is allowed, because it is a constant (= 1.4142...etc)
Hello from MrBillDoesMath!
Answer:
sin(A) = k/c
sin(C) = k/a
Discussion:
By definition of sine
,
sin(A) = side opposite angle / hypotenuse = k/c
sin(C) = side opposite angle/ hypotenuse = k/a
Added remark:
From the first equation, k = c sin(A). From the second equation k = asin(C). Hence.
asin(C) = csin(A) => divide both sides by "ac"
sin(C)/ c = sin(A)/a
Which is the law of sines for a triangle.
Thank you,
MrB
