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User:Graemeb1967
sin
2
θ
+
cos
2
θ
=
1.
{\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1.\!}
1
+
tan
2
θ
=
sec
2
θ
{\displaystyle 1+\tan ^{2}\theta =\sec ^{2}\theta \,}
and
1
+
cot
2
θ
=
csc
2
θ
{\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta \,}
x
1
=
x
0
−
f
(
x
0
)
f
′
(
x
0
)
=
10
−
10
2
−
612
2
⋅
10
=
35.6
x
2
=
x
1
−
f
(
x
1
)
f
′
(
x
1
)
=
35.6
−
35.6
2
−
612
2
⋅
35.6
=
2
_
6.3955056
x
3
=
⋮
=
⋮
=
24.7
_
906355
x
4
=
⋮
=
⋮
=
24.7386
_
883
x
5
=
⋮
=
⋮
=
24.7386338
_
{\displaystyle {\begin{matrix}x_{1}&=&x_{0}-{\dfrac {f(x_{0})}{f'(x_{0})}}&=&10-{\dfrac {10^{2}-612}{2\cdot 10}}&=&35.6\quad \quad \quad {}\\x_{2}&=&x_{1}-{\dfrac {f(x_{1})}{f'(x_{1})}}&=&35.6-{\dfrac {35.6^{2}-612}{2\cdot 35.6}}&=&{\underline {2}}6.3955056\\x_{3}&=&\vdots &=&\vdots &=&{\underline {24.7}}906355\\x_{4}&=&\vdots &=&\vdots &=&{\underline {24.7386}}883\\x_{5}&=&\vdots &=&\vdots &=&{\underline {24.7386338}}\end{matrix}}}