(4a/20+5a/20)*a^2/9 = 9a/20 * a^2/9= a^3/20 = 7.8^3/20 = 7.8*7.8*7.8/20 = 23.7278
Функция <em>sin t </em>нечетная: <em>sin</em>(-<em>t</em>) = - <em>sin t, </em>
функция<em> </em><em>cos t </em>четная: <em>cos</em>(-<em>t</em>) = <em>cos t</em>;
функции <em>sin t </em>и <em>cos t - </em>периодические, 2<span><span /></span> - основной период:
<span><span><span>sin</span><span>(</span><span>t</span><span /><span><span>2</span></span><span>k</span><span>)</span><span><span>=</span></span><span><span>s</span></span><span>int</span></span></span> и <span><span><span>cos</span><span>(</span><span>t</span><span /><span><span>2</span></span><span>k</span><span>)</span><span><span>=</span></span><span><span>c</span></span><span>ost</span></span></span>, где <em>k</em> - любое целое число;
область значений функций <em>sin t </em>и <em>cos t - </em>отрезок [ -1; 1];
функция <em>y</em> = <em>sin t </em>возрастает на промежутках <span><span><span><span><span /><span>−</span><span><span><span>2</span></span></span><span><span /></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span><span><span>2</span></span></span><span><span /></span></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>
и убывает на промежутках <span><span><span><span><span /><span><span><span>2</span></span></span><span><span /></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span><span><span>2</span></span></span><span><span><span>3</span></span><span /></span></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>, <span><span><span>k</span><span /><span><span>Z</span></span></span></span>;
функция <em>y</em> = <em>cos t </em>убывает на промежутках <span><span><span><span><span /><span>2</span><span>k</span><span>;</span><span /><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>
и возрастает на промежутках <span><span><span><span><span /><span>−</span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>, <span><span><span>k</span><span /><span><span>Z</span></span></span></span>.
1)cosx-sinx=1+2sinx*cosx возведем в квадрат
(cosx-sinx)²=(1+sin2x)²
1-2sinx*cosx=(1+sin2x)²
1-sim2x=1+2sin2x+sin²2x
sin²2x+3sinx=0
sin2x(sin2x+3)=0
sin2x=0 sin2x=-3 не имеет решений
2х=π*k, k∈Z
x=π/2*k
2)<span>1-sin2x=cosx-sinx
</span>sin²x-2sinx*cosx+cos²x=(cosx-sinx)
(cosx-sinx)²=(cosx-sinx)
(cosx-sinx-1)(cosx-sinx)=0
cosx=sinx
ctgx=1
x=π/4 + 2π,n ∈ Z,
x=5π/4+2π,n ∈<span> Z.
</span>cosx-sinx-1=0
cosx-sinx=1 возведем в квадрат
1-2sinx*cosx=1
-sin2x=0
sin2x=0
2х=π*k, k∈Z
<span>x=π/2*k</span>
Решение
cos(πx/8) = √2/2
πx/8 = (+ -) π/4 + 2πk, k∈Z
πx = (+ -) 2π + 16πk, k∈Z
x = (+ -) 2 + 16k, k∈Z
Наибольший отрицательный корень (- 2)
