trigonometry · worked example

Solve sin(45°) = √2/2

Method: sudut istimewa. Verified step-by-step solution with our free AI math solver.
Problem

sin(45°)\sin(45°)

Step-by-step solution

  1. Dalam segitiga siku-siku sama kaki 4545-4545-9090, sisi depan / sisi miring = 12\frac{1}{\sqrt{2}}.

  2. Rasionalkan: 1222=22\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}.

  3. Pada lingkaran satuan di 45°45°, baik x maupun y sama dengan 22\frac{\sqrt{2}}{2} — ini menegaskan jawabannya.

Answer

sin(45°)=22\sin(45°) = \tfrac{\sqrt{2}}{2}

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