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3 years ago

Find sin(2x), cos(2x) and tan (2x) from the given information. cot(x)=2/3, x in quadrant I

Mathematics

1 answer:

Usimov [2.4K]3 years ago

4 0

Answer:

1.) 6√13/13

2.) 4√13/13

3.) 3

Step-by-step explanation:

given that cot(x) = 2/3

But cot(x) = 1/tan(x)

Substitutes 1/tan(x) for cot(x)

1/tan(x) = 2/3

Reciprocate both sides

Tan(x) = 3/2 = opposite/adjacent

Use pythagorean theorem to find the hypothenus.

Hypothenus = sqrt ( 3^2 + 2^2 )

Hypothenus = sqrt ( 9 + 4 )

Hypothenus = sqrt (13)

Hypothenus = √13

1.) Sin(x) = opposite/hypothenus = 3/√13

Rationalise

3/√13 × √13/√13

3√13/13

Sin(2x) = 2 × 3√13/13

Sin(2x) = 6√13/13

2.) Cos( x ) = adjacent/hypothenus

Cos (x) = 2/√13

Rationalise

2/√13 × √13 /√13

2√13/13

Cos(2x) = 2 × 2√13/13

Cos(2x) = 4√13/13

3.) Tan (x) = 3/2

tan (2x) = 2 × 3/2

Tan(2x) = 3

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<h2><u>Answer with explanation</u>:</h2>

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Since $H_a$ is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

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For $n=95,\ \overline{x}=5483\ \&\ \sigma=500$ , we have

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$z_{0.06}=1.5548$

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[We reject the null hypothesis when critical value is less than the test statistic value .]

Conclusion : We have enough evidence at 0.06 significance level to support the claim that the new filament yields a longer bulb life

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4 years ago

a rectangle with a length of 9 inches and a width of 8 inches is divided in to squares of with sides of length 1 inch.One third

Mice21 [21]

Answer:

Step-by-step explanation:

rectangle = 8x9 = 72

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1/8 of 48 =6 48-6 =42

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green-----6

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3 years ago

Rate of change (0,0) and (5,5)

Tatiana [17]

The rate of change is 1.
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3 years ago

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The answer is

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3 years ago

Find the inverse of y=1/2x+6. Show steps

soldi70 [24.7K]

Answer:

y = 2x - 12

Step-by-step explanation:

To find the inverse of a function, you switch x and y and solve for y.

x = 1/2 y + 6 switch x and y

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3 years ago