Sign In
Ask Question
Sariah Hammond
Mathematics
13 May, 08:33
For which value of e is sin e=-1
+5
Answers (
1
)
Annie Villanueva
13 May, 08:59
0
=ei x
Step-by-step explanation:
Consider the function on the right hand side (RHS)
f (x) = cos (x) + i sin (x)
Differentiate this function
f ' (x) = - sin (x) + i cos (x) = i f (x)
So, this function has the property that its derivative is i times the original function.
What other type of function has this property?
A function g (x) will have this property if
dg / dx = i g
This is a differential equation that can be solved with seperation of variables
(1/g) dg = i dx
integral (1/g) dg = integral i dx
ln| g | = i x + C
| g | = ei x + C = eC ei x
| g | = C2 ei x
g = C3 ei x
So we need to determine what value (if any) of the constant C3 makes g (x) = f (x).
If we set x=0 and evaluate f (x) and g (x), we get
f (x) = cos (0) + i sin (0) = 1
g (x) = C3 ei 0 = C3
These functions are equal when C3 = 1.
Therefore,
cos (x) + i sin (x) = ei x
Comment
Complaint
Link
Know the Answer?
Answer
Not Sure About the Answer?
Find an answer to your question 👍
“For which value of e is sin e=-1 ...”
in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
Which fraction is equivalent to 4/5
Answers (2)
Is 10 greater than-2
Answers (2)
Chico walks 3/5 mile to the library. Nikki walks 1/4 the distance that Chico walks to the library.
Answers (1)
66,056 divided by four.
Answers (1)
Express the product of x+1 and x+8 in standard quadratic form.
Answers (2)
New Questions in Mathematics
A 21-foot flagpole casts a shadow. The distance along the ground from the base of the pole to the top of the shadow is 11 feet. What is the distance from the top of the pole to the tip of the shadow?
Answers (1)
What is the surface area of a radio that is 7 in by 11 in by 2 in
Answers (1)
Ten children are to be divided into an a team and a b team of 5 each. the a team will play in one league and the b team in another. how many different divisions are possible?
Answers (1)
What is 656 divided by 78
Answers (2)
What is the least common multiple for 165 and 22?
Answers (1)
Home
»
Mathematics
» For which value of e is sin e=-1
Sign In
Sign Up
Forgot Password?