Latihan Matematika Wajib Kelas X Nilai Rasio Trigonometri Sudut-Sudut Istimewa
# 8
Pilgan

Nilai dari sin⁡60°+sin⁡30°cos⁡60°+sin⁡90°=....\frac{\sin60\degree+\sin30\degree}{\cos60\degree+\sin90\degree}=....

A

13(3+1)\frac{1}{3}\left(\sqrt{3}+1\right)

B

13(3+2)\frac{1}{3}\left(\sqrt{3}+2\right)

C

12(2+1)\frac{1}{2}\left(\sqrt{2}+1\right)

D

13(3−1)\frac{1}{3}\left(\sqrt{3}-1\right)

E

12(3−2)\frac{1}{2}\left(\sqrt{3}-2\right)

Pembahasan:

Karena sin⁡30°=12\sin30\degree=\frac{1}{2} , sin⁡60°=123\sin60\degree=\frac{1}{2}\sqrt{3} , sin⁡90°=1\sin90\degree=1 , dan cos⁡60°=12\cos60\degree=\frac{1}{2} , maka

sin⁡60°+sin⁡30°cos⁡60°+sin⁡90°=123+1212+1\frac{\sin60\degree+\sin30\degree}{\cos60\degree+\sin90\degree}=\frac{\frac{1}{2}\sqrt{3}+\frac{1}{2}}{\frac{1}{2}+1}

=123+1232=\frac{\frac{1}{2}\sqrt{3}+\frac{1}{2}}{\frac{3}{2}}

=12(3+1)×23=\frac{1}{2}\left(\sqrt{3}+1\right)\times\frac{2}{3}

=13(3+1)=\frac{1}{3}\left(\sqrt{3}+1\right)

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