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3 years ago

Write cos(3x) - cos x as a product

Mathematics

1 answer:

sineoko [7]3 years ago

3 0

Answer:

-2sin(x) * sin(2x)

or any equivalent form, such as 4cos(x)[cos²(x)-1]

Step-by-step explanation:

simplify cos(3x) first:

cos(3x) = cos(2x+x) = cos(2x)cos(x) -sin(2x)sin(x)

using trig identities

= [2cos²(x)-1]cos(x) - [2sin(x)cos(x)]sin(x)

= 2cos³(x) - cos(x) - 2sin²(x)cos(x)

substituting using trig identity sin²(x) + cos²(x) = 1

2cos³(x) - cos(x) - 2[1-cos²(x)]cos(x)

2cos³(x) - cos(x) - 2cos(x)+2cos³(x)

4cos³(x) - 3cos(x)

remember this cos(3x), we still have to subtract cos(x)

4cos³(x) - 3cos(x) - cos(x) = 4cos³(x) - 4cos(x)

we can factor 4cos(x) to write this as a product of:

4cos(x)[cos²(x)-1]

further simplification if you want

trig identity sin²(x) + cos²(x) = 1

simplifying: sin²(x) = 1-cos²(x)

simplifying: -sin²(x) = cos²(x)-1

4cos(x)[cos²(x)-1]

4cos(x)[-sin²(x)]

-4cos(x)sin²(x)

trig identity: sin(2a) = 2cos(a)sin(a)

-2sin(x) * 2cos(x)sin(x)

-2sin(x)*sin(2x)

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Jackie’s test scores for the first semester are listed below.

jek_recluse [69]

Answer:

The answer is 91

Step-by-step explanation:

90 x 6 = 540

The numbers need to equal 540 all together to make an average of 90.

97 + 86 + 83 + 95 + 88 = 449

540 - 449 = 91

To check:

97 + 86 + 83 + 95 + 88 + 91 = 540

Therefore, the answer is 91

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3 years ago

Round each to the nearest cent.<br> $1,145.343<br> and<br> $264.5176

Arte-miy333 [17]

Answer:

$1,145.343 = $1,145.34

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3 years ago

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Help me solve this problem

Aleks04 [339]

I believe 1/9=9, 2/9=18, 3/9=27, 4/9=36
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3 years ago

Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1

Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

$P(x=r)=^nC_rp^rq^{n-r}$

(a) Exactly two will be drunken drivers.

$P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}$

$P(x=2)=66(0.2)^{2}(0.8)^{10}$

$P(x=2)=\approx 0.28347$

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

$P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)$

$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

$P(x=3\text{ or }x=4)=0.236223+0.132876$

$P(x=3\text{ or }x=4)\approx 0.369099$

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

$P(x\leq 7)=1-[0.9961]$

$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

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3 years ago

Nina earns $117.60$117.60 for 1414 hours of work.

pochemuha

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3 years ago