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# Greatest value of Sin4?T + cos4?T is

Greatest value of Sin4Θ + cos4Θ is

### 2 Answers by Expert Tutors

Ira S. | Bilingual math tutor and much moreBilingual math tutor and much more
5.0 5.0 (248 lesson ratings) (248)
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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.

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

Deanna L. | Electrical engineering major and music lover with MIT degreeElectrical engineering major and music l...
4.9 4.9 (122 lesson ratings) (122)
0
The greatest value of sin or cos is one. The catch is when sin is one cosine is zero and vicecovers a. So the answer is one.