Q.usuka sin(60°) × cos(60°) + csc(30°) _______layar belah ...

Q.usuka sin(60°) × cos(60°) + csc(30°) _______layar belah …

$boxed{bf{sin(60circ)times cos(60circ)+csc(30circ)=boxed{bf{frac{1}{4}sqrt{3}+2}}}}$

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Trigonometri

Pendahuluan

A.) Definisi

.) Perbandingan Trigonometri

Pada segitiga siku-siku ABC, berlaku :

$smallmathbf{left(a.right) sinalpha=frac{y}{r}=frac{de}{mi}}$

$smallmathbf{left(b.right) cosalpha=frac{x}{r}=frac{sa}{mi}}$

$smallmathbf{left(c.right) tanalpha=frac{y}{x}=frac{de}{sa}}$

$smallmathbf{left(d.right) cscalpha=frac{1}{sinalpha}=frac{r}{y}}$

$smallmathbf{left(e.right) secalpha=frac{1}{cosalpha}=frac{r}{x}}$

$smallmathbf{left(f.right) cotalpha=frac{1}{tanalpha}=frac{y}{x}}$

$:$

B.) Sudut dan Kuadran

1.) Pembagian Daerah

$boxed{begin{array}{c|c|c|c|c}underline{mathbf{Kuadran}}&underline{mathbf{I}}&underline{mathbf{II}}&underline{mathbf{III}}&underline{mathbf{IV}}\&&&\mathbf{absis(x)}&mathbf{+}&mathbf{-}&mathbf{-}&mathbf{+}\&&&\mathbf{Ordinat(y)}&mathbf{+}&mathbf{+}&mathbf{-}&mathbf{-}end{array}}$

2.) Tanda-tanda Fungsi

$boxed{begin{array}{c|c|c|c|c}underline{mathbf{Kuadran}}&underline{mathbf{I}}&underline{mathbf{II}}&underline{mathbf{III}}&underline{mathbf{IV}}\&&&\mathbf{sin}&mathbf{+}&mathbf{+}&mathbf{-}&mathbf{-}\&&&\mathbf{cos}&mathbf{+}&mathbf{-}&mathbf{-}&mathbf{+}\&&&\mathbf{tan}&mathbf{+}&mathbf{-}&mathbf{+}&mathbf{-}end{array}}$

3.) Sudut-sudut Istimewa

$boxed{begin{array}{c|c|c|c|c}underline{mathbf{Kuadran}}&underline{mathbf{0^{circ}}}&underline{mathbf{30^{circ}}}&underline{mathbf{45^{circ}}}&underline{mathbf{60^{circ}}}\&&&\mathbf{sin}&mathbf{0}&mathbf{frac{1}{2}}&mathbf{frac{1}{2}sqrt{2}}&mathbf{frac{1}{2}sqrt{3}}\&&&\mathbf{cos}&mathbf{1}&mathbf{frac{1}{2}sqrt{3}}&mathbf{frac{1}{2}sqrt{2}}&mathbf{frac{1}{2}}\&&&\mathbf{tan}&mathbf{0}&mathbf{frac{1}{3}sqrt{3}}&mathbf{1}&mathbf{sqrt{3}}end{array}}$ $boxed{begin{array}{c}underline{mathbf{90^{circ}}}\\mathbf{1}\\mathbf{0}\\inftyend{array}}$

4.) Sudut Berelasi

a. Kalau kita gunakan (90°± …) atau (270°± …)

1.) Fungsi berubah

$boxed{begin{array}{c|c}underline{mathbf{Mula-mula}}&underline{mathbf{Perubahan}}\\mathbf{sin}&mathbf{+/-cos}\\mathbf{cos}&mathbf{+/-sin}\\mathbf{tan}&mathbf{+/-cot}end{array}}$

2.) Tanda +/- mengikuti kuadran

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b. kalau kita gunakan (180°± …) atau (360°− …)

1.) Fungsi tetap

$boxed{begin{array}{c|c}underline{mathbf{Mula-mula}}&underline{mathbf{Perubahan}}\\mathbf{sin}&mathbf{+/-sin}\\mathbf{cos}&mathbf{+/-cos}\\mathbf{tan}&mathbf{+/-tan}end{array}}$

$:$

Pembahasan

Diketahui :

sin(60°) × cos(60°) + csc(30°)

Ditanya :

Hasil dari tersebut?

Jawaban :

$mathbf{sinleft(60circright)=frac{1}{2}sqrt{3}}$

$mathbf{cosleft(60 circ right)=frac{1}{2}}$

$begin{aligned} mathbf{cscleft(30 circ right) } &mathbf{=frac{1}{sinleft(30right)}}\ mathbf{cscleft(30 circ right) } &mathbf{=frac{1}{frac{1}{2}}}\ mathbf{cscleft(30 circ right) } &mathbf{=2} end{aligned}$