use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine . . sin^6 x

1 answer:

andrey2020 [161]2 years ago

4 0

1/128 (3 - 4 Cos[4 x] + Cos[8 x])( sin^2(x) )^2 cos^4(x)

( (1 - cos^2(x) )^2 cos^4(x) 

(1 - 2cos^2(x) + cos^4(x) ) cos^4(x) 

cos^4(x) - 2cos^6(x) + cos^8(x) 

( cos^2(x) )^2 - 2( cos^2(x) )^3 + ( cos^2(x) )^4 <==> knowing the identity; cos^2(x) = (1/2) * (1 + cos(2x)) 

( (1/2) * (1 + cos(2x)) )^2 - 2( (1/2) * (1 + cos(2x)) )^3 + ( (1/2) * (1 + cos(2x)) )^4 

( (1/4) * (1 + 2cos(2x) + cos^2(2x) )) - 2( (1/8) * (cos^3(2x) + 3cos^2(2x) + 3cos(2x) + 1) + ( (1/16) * cos^4(2x) + 4cos^3(2x) + 6cos^2(2x) + 4cos(2x) + 1)

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Which simplifications of the powers of i are correct? There may be more than one correct answer.

fredd [130]

$\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^{22}\implies i^{(4\cdot 5)+2}\implies i^{4\cdot 5}i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^{11}\implies i^{(2\cdot 5)+1}\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark$

$\bf i^{21}\implies i^{(4\cdot 5)+1}\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^{12}\implies i^{3\cdot 4}\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^{20}\implies i^{4\cdot 5}\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^{26}\implies i^{(4\cdot 6)+2}\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^{27}\implies i^{(4\cdot 6)+3}\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes$

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2 years ago

What term generally describes small chunks of rocks and debris in space? meteorites meteoroids meteors meteorides

deff fn [24]

Answer:

meteoroids

Step-by-step explanation:

5 0

2 years ago

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Which of the following is a trinomial with a constant term? A. 4x4 + 2x2 - 2x B. -3 + 4x4 C. 2x2 - 5 + x D. 4x4 - 3x2 + x

castortr0y [4]

C. 2x² - 5 + x is a trinomial with a constant term
That polynomial has three terms: (2x²), (-5) and (x)
Term (-5) contains no variable, so this is a constant term.

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2 years ago

What is the length of the hypotenuse of a right triangle with sides that measure 5 in. and 12 in

Vaselesa [24]

The answer is thirteen (13). You can use the Pythagorean theorem to figure it out.

a^2+b^2=c^2
5^2+12^2=c^2
25+144=c^2
169=c^2
13=c

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2 years ago

Fine the difference (2ab-5a-7)-(-5ab-7)

serg [7]

Answer:

7ab - 5a

Step-by-step explanation:

For addition and subtraction this type of variable we should always keep one thing in mind that, we can only add or subtract only those digits whose variables are the same.

Solving given equation step to step:

(2ab - 5a - 7) - (-5ab - 7)

Opening the bracket first,

⇒ 2ab - 5a - 7 - (- 5ab) - (- 7)

⇒ 2ab - 5a - 7 + 5ab + 7

Now, taking same variables digits together

⇒ (2 + 5)ab - 5a - 7 + 7

⇒ 7ab - 5a - 0

⇒ 7ab - 5a

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2 years ago