20 uždavinys

Sprendimas:

$$5\cdot sin(30)-cos(2\cdot 30)+1 = 5\cdot sin(30)-cos(60)+1 = \frac{5\cdot 1}{2}-\frac{1}{2}+1 = \frac{5}{2}+\frac{1}{2} = 3$$

Atsakymas: 3

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Sprendimas:

f(x) = $$5\cdot sin(x)-cos(2\cdot x)+1$$ 

$$cos(2\cdot x) = cos(x)^{2}-sin(x)^{2}$$ 

$$5\cdot sin(x)-cos(2\cdot x)+1$$ = 

$$5\cdot sin(x)-(cos(x)^{2}-sin(x)^{2})+1$$  =

$$5\cdot sin(x)-cos(x)^{2}+sin(x)^{2}+1$$  =

$$5\cdot sin(x)+sin(x)^{2}+1-cos(x)^{2}$$ =

$$5\cdot sin(x)+sin(x)^{2}+sin(x)^{2}$$  =

$$5\cdot sin(x)+2\cdot sin(x)^{2}$$ =

$$2\cdot sin(x)\cdot (2.5+sin(x))$$

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Sprendimas:

$$sin(x) = 0$$

$$x = \pi\cdot k$$

$$sin(x)+2.5 = 0$$

$$sin(x) = -2.5$$, šaknų nėra

Atsakymas: -180°; 0°; 180°

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Sprendimas:

f(-x) = $$2\cdot sin(-x)\cdot (2.5+sin((-x))) = -2\cdot sin(x)\cdot (2.5-sin(x))$$

negavome nei f(x), nei -f(x)

Atsakymas: nei lyginė, nei nelyginė