Matematika Sekolah Menengah Atas Quiz(+50)________________Soal pada gambar .....Selamat mengerjakan ....​

nevapacochaulv – March 25, 2023

Quiz(+50)

________________

Soal pada gambar .....
Selamat mengerjakan ....​

❐ Trigonometri

[tex] \rm \to \dfrac{11}{16} [/tex]

_____________________________

Pembahasan

[tex] sin~\theta + cos~\theta = \dfrac {1}{2} [/tex]

[tex] (sin~\theta + cos~\theta)² = \dfrac {1}{4} [/tex]

[tex] sin²\theta + cos²\theta + 2~sin~\theta~cos~\theta = \dfrac {1}{4} [/tex]

[tex] \rm 1 + 2~sin~\theta~cos~\theta = \dfrac{1}{4} [/tex]

[tex] \rm sin~\theta~cos~\theta = -\dfrac{3}{8} [/tex]

Jabarkan,

[tex] \rm = sin³\theta + cos³\theta [/tex]

[tex] \rm = (sin~\theta + cos~\theta)³ - 3(sin~\theta~cos~\theta)(sin~\theta + cos~\theta) [/tex]

[tex] \rm = (\frac{1}{2})³ - 3(-\frac{3}{8})(\frac{1}{2}) [/tex]

[tex] \rm = \dfrac {1}{8} + \dfrac{9}{8}~.~\dfrac{1}{2} [/tex]

[tex] \rm = \dfrac {1}{8} + \dfrac {9}{16} [/tex]

[tex] \rm = \dfrac {11}{16} [/tex]

[answer.2.content]