segment with the positiv
direction of x-axis is 30°
[NCERT EXEMPLAR
3. Find the equation of the line whose perpendicular distance from the origin is 4 units an
the angle which the normal makes with the positive direction of x-axis is 15° INCERT
Find the
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Answer:
Use normal form, xCosα+ySinα=p⟹(1)
p=4 and α=15⁰
Cos15⁰=Cos(45⁰−30⁰)
=Cos45⁰Cos30⁰+Sin45⁰Sin30⁰
=
2
1
2
3
+
2
1
2
1
=
2
2
3+1
Sin15⁰=
[1−Cos²15⁰]
=
2(
2
)
2
1−(
3+1
)²
=
8
(1−(3+1+2)
3
=
8
(8−4−2)
3
=
8
(4−2)
3
=
2
2
(4−2)
3
put Sin15⁰,Cos15⁰,p=4 in equation (1)
x[Cos15]+y[Sin15]=4
x[(
3+1
)]+y[4−2
3
]=4∗2
2
x[(
3+1
)]+y[4−2
3
]=8
2
Step-by-step explanation:
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