10.1

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(3)

y = x^4+x^3+ax, has axis // Oy (III Soros Olympiad 1996-97 R1 10.1)

Source:

a

does the graph of the function

y = x^4+x^3+ax

have an axis of symmetry parallel to the axis

Oy

geometryanalytic geometry

1^o in terms of cos 157^o = a (III Soros Olympiad 1996-97 R2 10.1)

Source:

It is known that

\cos 157^o = a

a

is given. Calculate

1^o

a

min n, sin n = sin (1997n) (III Soros Olympiad 1996-97 R3 10.1)

Source:

Find the smallest natural number

n

for which the equality

\sin n^o= \sin (1997n)^o

trigonometryalgebra