Question

QUIZZZ

Jika cos x = 2sin x , maka nilai cos x(sin x) adalah ........

a) [tex]\frac{\sqrt{5}}{2}[/tex]
b) [tex]\frac{2}{\sqrt{2}}[/tex]
c) ½
d) ⅔
e) ⅖

​

Answer 1

Jawaban:

[tex]\rm E.\frac{2}{5}[/tex]

Penjelasan:

[tex]\rm \cos\x=2\sin\x[/tex]

[tex]\rm \frac{\cos\x}{\sin\x}=2[/tex]

[tex]\rm \frac{\sin\x}{\cos\x}=\frac{1}{2}[/tex]

[tex]\rm \tan\x=\frac{1}{2}[/tex]

[tex]\rm \frac{de}{sa}=\frac{1}{2}\\[/tex]

[tex]\rm mi=\sqrt{de^2+sa^2}=\sqrt{1^2+2^2}=\sqrt{5}\\[/tex]

=====

[tex]\rm (de=1),(mi=\sqrt{5}),(sa=2)\\[/tex]

=====

[tex]\rm \cos\x(\sin\x)=\frac{sa}{mi}(\frac{de}{mi}[/tex]

[tex]\rm =\frac{2}{\sqrt{5}}(\frac{1}{\sqrt{5}}=\frac{2}{5}...E[/tex]

Answer 2

Verified answer

Jawab:

E

Penjelasan dengan langkah-langkah:

[tex]\begin{aligned}\cos x&\:=2\sin x\\\frac{\cos x}{\sin x}\:&=2\\\cot x\:&=2\\\frac{a}{b}\:&=\frac{2}{1}\end{aligned}[/tex]

Tentukan sin x dari rumus Pythagoras

[tex]\begin{aligned}c&\:=\sqrt{a^2+b^2}\\\:&=\sqrt{2^2+1^2}\\\:&=\sqrt{5}\end{aligned}[/tex]

sehingga

[tex]\begin{aligned}\sin x&\:=\frac{b}{c}\\\:&=\frac{1}{\sqrt{5}}\end{aligned}[/tex]

maka

[tex]\begin{aligned}\cos x\sin x&\:=2\sin x\sin x\\\:&=2\sin^2 x\\\:&=2\left ( \frac{1}{\sqrt{5}} \right )^2\\\:&=\frac{2}{5}\end{aligned}[/tex]