Search 83,587 tutors
FIND TUTORS
Ask a question
0 0

Greatest value of Sin4?T + cos4?T is

Tutors, please sign in to answer this question.

2 Answers

     Actually, the highest value for this sum is when cos 4ø = sin 4ø. cos 45 =s in45, just a fact that you may know. cos 45 =sqrt 2 /2, so sqrt 2 /2 + sqrt 2 /2 = sqrt 2 (approximately 1.414 . So if you're lookig for ø, 4ø = 45 and ø =11.25.

Comments

never mind it's (cos ø)^4
The first page reads sin 4ø but the second page reads (sin ø)^4 . If you mean the first case, my answer is correct, but if you mean the second case, Deanna's answer is correct .
2[(√2)/2]4 = 1/2
 
14 + 04 = 1
 
So I believe Deanna L.'s answer of 1 was correct
 
We can take the derivative to check.
 
4sin3 ΘcosΘ - 4cos3 ΘsinΘ= 0
 
critical numbers are 0, pi/4, and pi/2
 
0 and pi/2 give a maximum
 
pi/4 or 45 degrees is actually the minimum