diketahui sin (π-θ) = 5/13, θ sudut lancip maka nilai dari cot (π+θ) + cos(3/2π-θ) + cosec (2π+θ)...
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Jawab:
sin (π-θ) = sinθ
sinθ = 5/13 ==> y : r = 5 : 13 ==> x : y : r = 12 : 5 : 13
cot(π+θ)
= [tex]\frac{1}{tan(\pi +\theta)}[/tex]
[tex]=\frac{1}{tan\theta}[/tex]
[tex]=\frac{x}{y}[/tex]
[tex]=\frac{12}{5}[/tex]
cos(3/2π-θ)
= sin(1/2π-(3/2π-θ))
= sin(-π+θ)
= sin(2π-π+θ)
= sin(π+θ)
= -sinθ
[tex]=-\frac{y}{r}[/tex]
[tex]=-\frac{5}{13}[/tex]
cosec(2π-θ)
= cosec(-θ)
[tex]=\frac{1}{sin(-\theta)}[/tex]
[tex]=-\frac{1}{sin\theta}[/tex]
[tex]=-\frac{r}{y}[/tex]
[tex]=-\frac{13}{5}[/tex]
cot(π+θ) + cos(3/2π-θ) + cosec(2π-θ)
[tex]=\frac{12}{5}-\frac{5}{13} -\frac{13}{5}[/tex]
[tex]=\frac{156-25-169}{65}[/tex]
[tex]=-\frac{38}{65}[/tex]
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