Answer: 56.549 or 56.5
Explanation:
C= (pie) 3.14 * d = 2 * 3.14 * r
D= 18
C = 3.14 * 18 = 18 * 3.14
C = 56.549 or 56.5
Number 7 is 111 because they are alternate interior and 8 is 90
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
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Answer:
StartFraction pi Over 3 EndFraction
Step-by-step explanation:
we know that
The circumference of a circle subtends a central angle of 360 degrees or 2π radians
so
by proportion
Find out the central angle for an arc equal to One-sixth of the circumference of a circle
Let
x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference
Simplify
therefore
StartFraction pi Over 3 EndFraction
