Question

[Shinobu Kochou]

 

Answer 1

[Nguyễn Huy Tú]

a, \(sin^2x+cos^2x=1\Leftrightarrow cos^2x=1-\dfrac{9}{25}=\dfrac{16}{25}\Leftrightarrow cosx=\dfrac{4}{5}\)

\(tanx=\dfrac{sinx}{cosx}=-\dfrac{3}{5}:\left(\dfrac{4}{5}\right)=-\dfrac{3}{4}\)

\(cotx=-\dfrac{4}{3}\)

c, \(sin^2x+cos^2x=1\Leftrightarrow sin^2x=1-\dfrac{9}{25}=\dfrac{16}{25}\Leftrightarrow sinx=\dfrac{4}{5}\)

\(tanx=\dfrac{sinx}{cosx}=\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{4}{3}\)

\(cotx=\dfrac{3}{4}\)

b, \(cos^2x+sin^2x=1\Leftrightarrow sin^2x=1-\dfrac{1}{16}=\dfrac{15}{16}\Leftrightarrow sinx=\dfrac{\sqrt{15}}{4}\)

\(tanx=\dfrac{\sqrt{15}}{4}:\dfrac{1}{4}=\sqrt{15}\)

\(cotx=\dfrac{1}{\sqrt{15}}\)

d, \(sin^2x+cos^2x=1\Leftrightarrow sin^2x=1-\dfrac{25}{169}=\dfrac{144}{169}\Leftrightarrow sinx=\dfrac{12}{13}\)

\(tanx=\dfrac{12}{13}:\left(-\dfrac{5}{13}\right)=-\dfrac{12}{5}\)

\(cotx=-\dfrac{5}{12}\)

Answer 2

[Nguyễn Lê Phước Thịnh]

a: \(\Omega< x< \dfrac{3}{2}\Omega\)

=>cosx<0

Ta có: \(sin^2x+cos^2x=1\)

=>\(cos^2x=1-sin^2x=1-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}\)

mà cosx<0

nên \(cosx=-\dfrac{4}{5}\)

\(tanx=\dfrac{sinx}{cosx}=\dfrac{-3}{5}:\dfrac{-4}{5}=\dfrac{3}{4}\)

\(cotx=\dfrac{1}{tanx}=\dfrac{4}{3}\)

b: \(0< x< \dfrac{\Omega}{2}\)

=>sin x>0

\(sin^2x+cos^2x=1\)

=>\(sin^2x=1-\left(\dfrac{1}{4}\right)^2=\dfrac{15}{16}\)

mà sin x>0

nên \(sinx=\dfrac{\sqrt{15}}{4}\)

\(tanx=\dfrac{sinx}{cosx}=\dfrac{\sqrt{15}}{4}:\dfrac{1}{4}=\sqrt{15}\)

\(cotx=\dfrac{1}{tanx}=\dfrac{1}{\sqrt{15}}=\dfrac{\sqrt{15}}{15}\)

c: 0<x<90 độ

=>sin x>0

\(sin^2x+cos^2x=1\)

=>\(sin^2x=1-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}=\left(\dfrac{4}{5}\right)^2\)

mà sin x>0

nên \(sinx=\dfrac{4}{5}\)

\(tanx=\dfrac{sinx}{cosx}=\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{4}{3}\)

\(cotx=1:\dfrac{4}{3}=\dfrac{3}{4}\)

d: \(180^0< x< 270^0\)

=>sin x<0

\(sin^2x+cos^2x=1\)

=>\(sin^2x=1-\left(-\dfrac{5}{13}\right)^2=1-\dfrac{25}{169}=\dfrac{144}{169}\)

mà sin x<0

nên \(sinx=-\dfrac{12}{13}\)

\(tanx=\dfrac{sinx}{cosx}=\dfrac{-12}{13}:\dfrac{-5}{13}=\dfrac{12}{5}\)

\(cotx=\dfrac{1}{tanx}=\dfrac{5}{12}\)