# Trig

Find
[4(cos115+isin115)]^6

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2. 👎 0
3. 👁 96
1. 4^6=4096
115*6=690
cos(690)=sqrt(3)/2
sin(690)=-1/2

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2. 👎 0
2. De Moivre's Theorem:

(r(cosØ + i sinØ))^n
= r^n(cos(nØ) + i sin(nØ))

in our case ....
[4(cos115+isin115)]^6
= 4^6( cos 690 + i sin 690)
I will assume my meant degrees, since the numbers work out nicely in degrees.
Now 690° is coterminal with 330° or -30°
sin(-30°) = -1/2, and cos(-30) = √3/2

so continuing...
= 4096(√3/2 - (1/2)i)

= 2048√3 - 2048

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posted by Reiny
3. oops, left out the i in the last line

= 2048√3 - 2048i

(I could always claim that you should have "imagined" it)

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2. 👎 0
posted by Reiny

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