Polynomial Exponent

Polynomial of a single term is called as Monomial. If the Polynomial has the two terms Sum or Difference then it is called a Bi-nomial, the Sums or Differences of a three-term Polynomial is called a Trinomial. The Sums and/or Differences of polynomial of four or more terms are simply called polynomial.

Two or more terms of a Polynomial exponent that has the equivalent variable and precisely the same whole number polynomial exponent are called Like Terms. For suitable example the terms; 6X3 and -7X3, are Like Terms, since the variable X is the similar variable in both terms, and the Whole number exponent, 3, is absolutely the similar polynomial exponent in both terms. The terms;4X3 and 4X4 are not Like Terms although the variable X is the same in both terms but the Whole number polynomial exponent are completely different from other.

Operation of polynomial exponent:

Addition of polynomial exponent:

Two or more polynomials, adding the terms,

Suitable example adding polynomial exponent,

Example1:

(2x2+3x3)+(x2+7x3)

=2x2+x2+3x3+7x3

The variable and exponent must be same then we add the polynomial exponent,

=3x2+10x3

So the result is  =3x2+10x3

Subtraction of polynomial exponent

Example2:

(3x2+3x3)-(x2+7x3)

=3x2-x2+3x3-7x3

The variable and exponent must be same then we subtract the polynomial exponent,

=2x2-4x3

So the result is =2x2-4x3

Multiplication of polynomial exponent:

Two or more polynomial, so multiply their exponent terms. For reasonable example to multiply the following two Terms, 2X2 and 7X2, Then the following terms then first multiply the coefficients (2) (7) and we multiply (X2) (X2) which can be expressed as the following term 14X4, that is, when we multiply variables that are the same.


Different variables in polynomial exponent:

The variables are different and the exponent also different, so we can write the variables and exponents adjoining to each other.

For Example, (7X2)(3Y2)is equal to 21X2Y2.

So the result is 21X2Y2

Similar to all the different variable, polynomial exponent.

To multiply the two polynomial exponent, for example (X-2Y)(X-2Y), then the result is x2-2xy+4y2 . Here we take the first term X of the first Binomial and multiply each term in the second Binomial, then we take the second term in the first Binomial and multiply each term in the second Binomial, and then we add all the terms. Similar to all the polynomial categories, for example trinomial, binomial exponents.

Inverse Trigonometry Definition

The three trigonometry functions are arcsin(x), arccos(x), arctan(x). The inverse trigonometry function is the inverse functions of the trigonometry, written as cos^-1 x , cot^-1 x , csc^-1 x , sec^-1 x , sin^-1 x , and tan^-1 x .

Sine:

H (x) = sin(x)   where   x is in [-pi/2 , pi/2]

Cosine:

G (x) = cos(x) where   x is in [0 , pi ]

Tangent:

F (x) = tan(x)   where   x is in (-pi/2 , pi/2 )

Understanding Inverse Trig Function is always challenging for me but thanks to all math help websites to help me out.

Cosecant Definition

Csc theta = (hypotenuse)/(opposite)

Secant Definition

Sec theta = (hypotenuse)/(adjacent)

Cotangent Definition

Cot theta = (adjacent)/(opposite)

Examples of Inverse trigonometry functions:

Example 1:

Find the angle of x in the below diagram. Give the answer in four decimal points.

Solution:

sin x =2.3/8.15

x = sin -1(2.3/8.15 )

= 16.3921˚

Example 2:

Solve sin(cos-1 x )

Solution:
Let z = sin ( cos-1 x ) and y = cos-1 x so that z = sin  y. y = cos-1 x may also be marked as


cos y = x with pi / 2 <= y <=- pi / 2

Also

sin2y + cos2y = 1

Substitute cos y by x and solve for cos y to obtain

sin y = + or - sqrt (1 - x^2)

But pi / 2  <= y <= - pi / 2 so that cos y is positive

z = sin y = sin(cos-1 x) = sqrt (1 - x^2)

Example 3:

Evaluate the following sin-1( cos ((7 pi) / 4 ))

Solution:
sin-1( cos ( y ) ) = y only for  pi / 2 <=  y <= -pi / 2 . So we initial transform the given expression noting that cos ((7pi) / 4 ) = cos (-pi / 4 ) as follows

sin-1( cos ((7 pi) / 4 )) = sin-1( cos ( pi / 4 ))  - pi / 4  was selected since it satisfies the condition  pi / 2 <=  y <= - pi / 2 . Hence

sin-1( cos ((7 pi) / 4 )) =pi/4

Example 4:

With the given value find inverse of tan.

Solution:

Since tangent, again, is the trig function associated with opposite and adjacent sides, we apply the inverse of tangent to calculate the measure of this angle.

Tan 16 = (opposite)/(adjacent)

Tan 16 = ((bar(AC))/(bar(CB)))

Tan-1(7/24 ) = 16 o