Question

What is the distance between the points A(sinθ – cosθ,0) and B(0,sin θ

+ cosθ)?
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Answer 1

Answer:

• The distance between points A and B is √2 units.

Step-by-step explanation:

Given that:

Two points.

• A(sin θ - cos θ, 0)
• B(0, sin θ + cos θ)

To Find:

• What is the distance between the points?

Finding the distance between the points:

Using distance formula.

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[{0 - (sin θ - cos θ)}² + (sin θ + cos θ - 0)²]

AB = √[(cos θ - sin θ)² + (sin θ + cos θ)²]

AB = √[sin² θ + cos² θ - 2 • sin θ • cos θ + sin² θ + cos² θ + 2 • sin θ • cos θ]

Cancelling 2 • sin θ • cos θ.

AB = √[sin² θ + cos² θ + sin² θ + cos² θ]

AB = √[1 + 1 ]

AB = √[2]

AB = √2

∴ The distance between the points = √2 units

Algebraic identities used:

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab

Trigonometric identities used:

• sin² θ + cos² θ = 1

Answer 2

Given Question

What is the distance between the points A(sinθ – cosθ,0) and B(0,sin θ

+ cosθ)?

Require answer

So distance between two points D = √{ (sinθ - cos θ)² +(cos θ+ sinθ)²}

D = √[ (sinθ )² + (cos θ)² - 2 sin θ cosθ +(cos θ )² + ( sin θ) ² +2 cos θ sinθ) ]

Since (sinθ )² + (cos θ)² = 1

Therefore

D= √[ ( 1 - 2 sin θ cosθ + 1 +2 cos θ sinθ) ]

Cancelling 2 sin θ cos θ and -2 cos θ sinθ)

D = √2