Find the equation of line whose perpendicular distance from the origin is 4 units and angle which the normal makes with positive direction of x - axis is 15
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Use normal form,
x Cos α + y Sin α = p .......(1)
p= 4 and α = 15⁰
Cos 15 ⁰ = Cos ( 45⁰ - 30⁰ )
=> Cos 45⁰ Cos 30⁰ + Sin45⁰ Sin30⁰
=> (1/√2) (√3/2) + (1/ √2) (1/2)
=> (√3 +1) / 2√2
Sin 15 ⁰ = √[1- Cos² 15⁰]
=> √ [ 1- (√3+1)²/〈2√2〉²]
=> √[ 1 - (3+ 1 +2√3)/8]
=> √[(8 - 4 - 2√3)/8]
=> √[ (4 - 2√3)/8]
=> √[4 -2√3] ÷ 2 √2
put Sin 15⁰ ,Cos 15⁰ , & p=4 in equation (1)
x [ Cos 15 ] + y [ Sin 15 ] = 4
x [ (√3 + 1 ) ] + y [ 4 - 2√3] = 4 * 2 √2
x [ (√ 3 + 1 ) ] + y [ 4 - 2√3 ] = 8 √ 2
x Cos α + y Sin α = p .......(1)
p= 4 and α = 15⁰
Cos 15 ⁰ = Cos ( 45⁰ - 30⁰ )
=> Cos 45⁰ Cos 30⁰ + Sin45⁰ Sin30⁰
=> (1/√2) (√3/2) + (1/ √2) (1/2)
=> (√3 +1) / 2√2
Sin 15 ⁰ = √[1- Cos² 15⁰]
=> √ [ 1- (√3+1)²/〈2√2〉²]
=> √[ 1 - (3+ 1 +2√3)/8]
=> √[(8 - 4 - 2√3)/8]
=> √[ (4 - 2√3)/8]
=> √[4 -2√3] ÷ 2 √2
put Sin 15⁰ ,Cos 15⁰ , & p=4 in equation (1)
x [ Cos 15 ] + y [ Sin 15 ] = 4
x [ (√3 + 1 ) ] + y [ 4 - 2√3] = 4 * 2 √2
x [ (√ 3 + 1 ) ] + y [ 4 - 2√3 ] = 8 √ 2
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