Odd functions are those that satisfy the condition
f(-x)=-f(x)
For example, check if x^3 is odd =>
f(x)=x^3
f(-x) = (-x)^3
-f(x)=-x^3
Since (-x)^3=-x^3, we see that f(x)=x^3 is an odd function.
In fact, polynomials which contain odd-powered terms only are odd. (constant is even)
As an exercise, you can verify that sin(x) is odd, cos(x) is even.
On graphs, odd functions are those that resemble a 180 degree rotation.
Check with graphs of above examples.
So we identify the first graph (f(x)=-x^3) is odd (we can identify a 180 degree rotation)
Odd functions have a property that the sum of individually odd functions is
also odd. For example, x+x^3-6x^5 is odd, so is x+sin(x).
For the next graph, f(x)=|x+2| is not odd (nor even) because if we rotate one part of the graph, it does not coincide with another part of the graph, so it is not odd.
For the last graph, f(x)=3cos(x), it is not odd, again because if we rotate about the origin by 180 degrees, we get a different graph. However, it is an even function because it is symmetrical about the y-axis.
Answer:
The answer is 27
Step-by-step explanation:
This is because each person can have up to three roles, and there are 9 students. So you can form an array, or a table to show your values. so if you have 9 rows and 3 coulombs and you can have 27 crosses in the array.
Step-by-step explanation:
cot x + 2 tan x + tan³ x
Write in terms of sine and cosine:
(cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)
Find the common denominator:
(cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))
Add:
(cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)
Factor:
(sin² x + cos² x)² / (sin x cos³ x)
Pythagorean identity:
1 / (sin x cos³ x)
Multiply top and bottom by cos x:
cos x / (sin x cos⁴ x)
Simplify:
cot x sec⁴ x
Answer:
Step-by-step explanation:
A tree that is 100 feet tall casts a shadow that is 150 feet long ...
The angle at which the ray of the sun hit the ground is that which has a tangent equal to 100 / 150 or 2/3. This angle is equal to 33.69. Thus, the answer is letter B. 34°
Answer:
A:x√ 7x² / 3
Step-by-step explanation:
