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2 years ago

Find the exact value of : cos(2 arctan(4/3))

1 answer:

7 0

Cos(2 arctan(4/3)) = cos(2 arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arcsin(4/5)) = (3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25.

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Factor completely. 21a^2 - 57a + 30

Kryger [21]

The answer is 3(a-2)(7a-5)

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3 years ago

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Mrs.tokalaka uses 9/10 of a can of coffe beans,each week.how many cans of beans does she use in 6 weeks? write your answer two d

Snowcat [4.5K]

9 x 6 = 54

so you can write it as
54/60
or = 22/30
= 11/15

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3 years ago

Integrate sin²2x cos²2xdx

Masteriza [31]

$\sin^2x=\dfrac{1-\cos2x}2$
$\cos^2x=\dfrac{1+\cos2x}2$

From the identities above, you have

$\sin^22x\cos^22x=\dfrac{(1-\cos4x)(1+\cos4x)}4=\dfrac{1-\cos^24x}4$

Applying once more, you have

$\dfrac{1-\cos^24x}4=\dfrac{1-\dfrac{1+\cos8x}2}4=\dfrac{1-\cos8x}8$

So,

$\displaystyle\int\sin^22x\cos^22x\,\mathrm dx=\frac18\int(1-\cos8x)\,\mathrm dx=\frac x8-\frac1{64}\sin8x+C$

3 0

3 years ago

Dawn has 5\6 yard of lace. She uses 4\5 of it on a dress and the rest on a jewel box. How much does she use on the jewel box

mr_godi [17]

Answer:

Jewelry box: 1/6 yard

Step-by-step explanation:

4/5 (not 4\5) of her 5/6 yard goes into a dress: (4/5)(5/6 yd) = 2/3 yard.

This is the same as 4/6 yard. The amount of lace remaining, to be used on a jewelry box, is 5/6 - 4/6, or 1/6 yard.

3 0

3 years ago

PLEASE HELP!!! I don’t understand

asambeis [7]

Answer:

Step-by-step explanation:

Use the half angle identity for cosine:

cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)

I'm going to figure out the sign part first for cos(x/2)...

so x is in third quadrant which puts x between 180 and 270

if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)

cosine is negative in the second quadrant

so we know that

cos(x/2)=-sqrt(1+cos(x))/sqrt(2)

Now we need cos(x)... since we are in the third quadrant cos(x) is negative...

If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.

So let's plug it in:

cos(x/2)=-sqrt(1+4/5)/sqrt(2)

No one likes compound fractions (mini-fractions inside bigger fractions)

Multiply top and bottom inside the square roots by 5.

cos(x/2)=-sqrt(5+4)/sqrt(10)

cos(x/2)=-sqrt(9)/sqrt(10)

cos(x/2)=-3/sqrt(10)

Rationalize the denominator

cos(x/2)=-3sqrt(10)/10

3 0

3 years ago