Question

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

Answer 1

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