[tex]sina=+\frac{3}{4} \\ \frac{\pi} {2} \ \textless \ a\ \textless \ \pi[/tex] Надо найти cosa, tga,ctga, tg2a. Created by 321NIYAZ123. algebra-ru

tex] Надо найти cosa, tga,ctga, tg2a...

321NIYAZ123 @321NIYAZ123

July 2022 1 31 Report

[tex]sina=+\frac{3}{4} \\ \frac{\pi} {2} \ \textless \ a\ \textless \ \pi[/tex]
Надо найти cosa, tga,ctga, tg2a

Answers & Comments

Artem112

Verified answer

Так как $\dfrac{\pi} {2}$ , то угол а - второй четверти, где косинус, тангенс и котангенс отрицательные.

$\sin^2a+\cos^2a=1\\\cos^2a=1-\sin^2a\\\cos a=-\sqrt{1-\sin^2a} \\\cos a=-\sqrt{1-\left(\dfrac{3}{4}\right)^2 } =-\sqrt{1-\dfrac{9}{16} } =-\sqrt{\dfrac{7}{16} } =-\dfrac{\sqrt{7}} {4}$

$\mathrm{tg}a=\dfrac{\sin a}{\cos a}=\dfrac{3} {4}:\left(-\dfrac{\sqrt{7}} {4} \right)=\dfrac{3} {4}\cdot\left(-\dfrac{4} {\sqrt{7}} \right)=-\dfrac{3} {\sqrt{7}} =-\dfrac{3\sqrt{7}} {7}$

$\mathrm{ctg}a=\dfrac{1}{\mathrm{tg}a} =1:\left(-\dfrac{3} {\sqrt{7}}\right) =-\dfrac{\sqrt{7}} {3}$

$\mathrm{tg}2a=\dfrac{2\mathrm{tg}a}{1-\mathrm{tg}^2a} =\dfrac{2\cdot\left(-\dfrac{3} {\sqrt{7}}\right)}{1-\left(-\dfrac{3} {\sqrt{7}}\right)^2} =\dfrac{-\dfrac{6} {\sqrt{7}}}{1-\dfrac{9} {7}} =\dfrac{-\dfrac{6} {\sqrt{7}}}{-\dfrac{2} {7}} =\\\\=\dfrac{6}{\sqrt{7}}:\dfrac{2} {7}=\dfrac{6}{\sqrt{7}}\cdot\dfrac{7} {2}=3\sqrt{7}$

1 votes Thanks 1

Answers & Comments

Verified answer

na odnom chertezhe izobrazheny dve detali 1 ya dlinnoj 6 sm a 2 ya kotoraya koroch

1 poluchite ammiak tremya raznymi sposobami

dajte nazvaniee veshestvam i ukazhite klass kazhdogo veshestva

krossvord na temu osnovy genetiki i selekciya

tex]...

polzovatel vvodit celochislennyj massiv iz 25 elementov vychislit summu eleme

2 postavte glagoly v nuzhnom vremeni aktivnogo zaloga sandy read historic bo

ch s kakoj skorostyu on shel po tropinke

v odnom splave 17 medi a v drugom 42 skolko kazhdogo splava nado vzyat cht

ch na vsyo puteshestvie ushlo 25 ch kakova srednyaya skorost turista

рекомендуемые вопросы

Helpful Links

Helpful Social