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Arturiano [62]
3 years ago
9

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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6 0
3 years ago
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trasher [3.6K]




sin(0) = opposite/hypotenuse = 2/5

cos(0) = adjacent/hypotenuse = sqrt21/5

tan(0) = opposite/adjacent = 2/sqrt21 * sqrt21/sqrt21 = 2sqrt21/21

cot(0) = adjacent/opposite = sqrt21/2

sec(0) = hypotenuse/adjacent = 5sqrt21/21

5 0
3 years ago
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