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Simplify without using tables and calculators sin 60° tan 30°

Mathematics

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Answer

12\frac{1}{2}

Step-by-step solution

4 steps

Ili kurahisisha usemi sin⁡60∘tan⁡30∘\sin 60^\circ \tan 30^\circ bila kutumia jedwali au kikokotoo, tutatumia thamani kamili za pembe maalum.

  1. Tambua thamani za sin⁡60∘\sin 60^\circ na tan⁡30∘\tan 30^\circ.

    Tunajua kwamba:

    sin⁡60∘=32\sin 60^\circ = \frac{\sqrt{3}}{2} tan⁡30∘=13\tan 30^\circ = \frac{1}{\sqrt{3}}

  2. Badilisha thamani hizi kwenye usemi uliotolewa.

    sin⁡60∘tan⁡30∘=(32)×(13)\sin 60^\circ \tan 30^\circ = \left(\frac{\sqrt{3}}{2}\right) \times \left(\frac{1}{\sqrt{3}}\right)

  3. Rahisisha usemi.

    32×13=323\frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{2\sqrt{3}}

  4. Futa 3\sqrt{3} kutoka kwa namba na denominata.

    323=12\frac{\sqrt{3}}{2\sqrt{3}} = \frac{1}{2}

    Jibu la mwisho ni:

    12\frac{1}{2}
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