2.6 KiB
Goniometrické funkce
x\in(0\degree;90\degree)
\sin\alpha=\frac{a}c (\sin\beta=\frac{b}c)
\cos\alpha=\frac{b}c (\sin\beta=\frac{a}c)
$\tg\alpha=\frac{a}b$
\cotg\alpha=\frac{b}a
V pravoúhlem \triangle ABC (C): \beta=38\degree; a=7cm, ostatní úhly a strany?
\alpha=180\degree-90\degree-\beta=90-38=52\degree
$\sin\alpha=0.98662759$
$\sin\alpha=\frac{a}c$
$0.98662759=\frac7c$
$c*0.98662759=7$
$c=\frac7{0.98662759}$
c=7,094875585224613cm
$\sin\beta=\frac{y_B}1=y_B$
\cos\beta=\frac{x_B}1=x_B
[!SENTENCE] Funkce sinus je taková funkce, která každému číslu/úhlu
\alpha\in\mathbb{R}přiřadí čísloy_A(viz obrázek nahoře)…$y$-ová souřadnice průsečíku A koncového ramena orientovaného úhlu\alpha.
Tabulka význačných hodnot
\alpha |
0\degree/0 |
30\degree/\frac\pi6 |
45\degree/\frac\pi4 |
60\degree/\frac\pi3 |
90\degree/\frac\pi2 |
|---|---|---|---|---|---|
\sin\alpha |
0 |
\frac12 |
\frac{\sqrt2}2 |
\frac{\sqrt3}2 |
1 |
\cos\alpha |
1 |
\frac{\sqrt3}2 |
\frac{\sqrt2}2 |
\frac12 |
0 |
40/6.3/8 (petakova)
a)
$\sin\frac56\pi=\sin\frac{5*\pi6}6=\sin(5\frac\pi6)=\sin(530\degree)=\sin(150\degree)=\sin(30\degree)=\frac12$
$\sin\frac{15}3\pi=\sin(15*60\degree)=\sin900\degree=0$
\sin(-\frac74\pi)=\sin(-7*45\degree)=\sin(450-135\degree)=\sin(315\degree)=-\sin(45\degree)=\frac{\sqrt2}2
b)
$\cos\frac34\pi=\cos(345\degree)=\cos(135\degree)=\sin(45\degree)=\frac{\sqrt2}2$
$\cos\frac76\pi=\cos(730\degree)=\cos(300-90)=\cos(210\degree)=-\sin(60\degree)=$
\cos(-\frac43\pi)
c)
$\sin210\degree=-\sin30\degree=-\frac12$
$\sin330\degree=-\sin30\degree=-\frac12$
\sin720\degree=0
d)
$\cos(-180\degree)=1$
$\cos120\degree=\sin60\degree=\frac{\sqrt3}2$
\cos240\degree=-\sin30\degree=-\frac12
$f_1: y=\sin x$
$f_1(0)=0$
$f_1(\frac\pi2)=1$
f_1(\frac\pi3)=0.5
$f_2:u=\sin x+2$
$f_1(0)=2$
$f_1(\frac\pi2)=3$
f_1(\frac\pi3)=2.5
f_3: y=\sin(x+2)
$f_4: y=2\sin x$
$f_4(0)=0$
$f_4(\frac\pi2)=2$
f_4(\frac\pi3)=1
