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Mathematics

Find the inclination of the line whose slope is:

(i) 0

(ii) 1

(iii) 3{\sqrt3}

(iv) 13\dfrac{1}{\sqrt3}

Coordinate Geometry

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Answer

(i) The slope of the line = m = 0 ⇒ tan θ = 0

⇒ tan θ = tan 0°

⇒ θ = 0°

Hence, the inclination is 0°.

(ii) The slope of the line = m = 1 ⇒ tan θ = 1

⇒ tan θ = tan 45°

⇒ θ = 45°

Hence, the inclination is 45°.

(iii) The slope of the line = m = 3{\sqrt3} ⇒ tan θ = 3{\sqrt3}.

⇒ tan θ = tan 60°

⇒ θ = 60°

Hence, the inclination is 60°.

(iv) The slope of the line = m = 13\dfrac{1}{\sqrt3} ⇒ tan θ = 13\dfrac{1}{\sqrt3}

⇒ tan θ = tan 30°

⇒ θ = 30°

Hence, the inclination is 30°.

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