Introduction to factoring trigonometric functions:
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Factorization (also factorization in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. (Source: Wikipedia)
Example Problems for Factoring Trigonometric Functions
Factoring trigonometric functions example problem 1:
Factoring the given trigonometric functions f (x) = cos^2x + 22cosx + 121
Solution:
Given equation is f (x) = cos^2x + 22cosx + 121
Factorize the given equation, we get
f (x) = cos^2x + 11cosx + 11cosx + 121
Grouping the first two terms and second two terms, we get
f (x) = (cos^2x + 11cosx) + (11cosx + 121)
Take common terms in outside, we get
f (x) = cosx (cosx + 11) + 11 (cosx + 11)
= (cosx + 11) (cosx + 11)
The factors of the given trigonometric equation is (cosx + 11)2
Answer:
The final answer is (cosx + 11)2
Factoring trigonometric functions example problem 2:
Factoring the given trigonometric equations g (x) = sin^2x - 12sinx + 20
Solution:
Given equation is g (x) = sin^2x - 12sinx + 20
Factorize the given equation, we get
= sin^2x - 10sinx - 2sinx + 20
Grouping the first two terms and second two terms, we get
= (sin^2x - 10sinx) - (2sinx - 20)
Take common terms in outside, we get
= sinx (sinx - 10) - 2 (sinx - 10)
= (sinx - 10) (sinx - 2)
The factors of the given trigonometric equation is (sinx - 10) and (sinx - 2)
Answer:
The final answer is (sinx - 10) and (sinx - 2)
Understanding Derivative of Absolute Value Function is always challenging for me but thanks to all math help websites to help me out.
Practice Problems for Factoring Trigonometric Functions
Factoring trigonometric functions practice problem 1:
Factoring the given trigonometric functions f (x) = cos^2x - 7cosx + 6
Answer:
The final answer is (cosx - 6) and (cosx - 1)
Factoring trigonometric functions practice problem 2:
Factoring the given trigonometric functions g (x) = sin^2x + 12sinx - 28
Answer:
The final answer is (sinx + 14) and (sinx - 2)
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Factorization (also factorization in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. (Source: Wikipedia)
Example Problems for Factoring Trigonometric Functions
Factoring trigonometric functions example problem 1:
Factoring the given trigonometric functions f (x) = cos^2x + 22cosx + 121
Solution:
Given equation is f (x) = cos^2x + 22cosx + 121
Factorize the given equation, we get
f (x) = cos^2x + 11cosx + 11cosx + 121
Grouping the first two terms and second two terms, we get
f (x) = (cos^2x + 11cosx) + (11cosx + 121)
Take common terms in outside, we get
f (x) = cosx (cosx + 11) + 11 (cosx + 11)
= (cosx + 11) (cosx + 11)
The factors of the given trigonometric equation is (cosx + 11)2
Answer:
The final answer is (cosx + 11)2
Factoring trigonometric functions example problem 2:
Factoring the given trigonometric equations g (x) = sin^2x - 12sinx + 20
Solution:
Given equation is g (x) = sin^2x - 12sinx + 20
Factorize the given equation, we get
= sin^2x - 10sinx - 2sinx + 20
Grouping the first two terms and second two terms, we get
= (sin^2x - 10sinx) - (2sinx - 20)
Take common terms in outside, we get
= sinx (sinx - 10) - 2 (sinx - 10)
= (sinx - 10) (sinx - 2)
The factors of the given trigonometric equation is (sinx - 10) and (sinx - 2)
Answer:
The final answer is (sinx - 10) and (sinx - 2)
Understanding Derivative of Absolute Value Function is always challenging for me but thanks to all math help websites to help me out.
Practice Problems for Factoring Trigonometric Functions
Factoring trigonometric functions practice problem 1:
Factoring the given trigonometric functions f (x) = cos^2x - 7cosx + 6
Answer:
The final answer is (cosx - 6) and (cosx - 1)
Factoring trigonometric functions practice problem 2:
Factoring the given trigonometric functions g (x) = sin^2x + 12sinx - 28
Answer:
The final answer is (sinx + 14) and (sinx - 2)
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